{"id":21502,"date":"2022-04-07T23:51:06","date_gmt":"2022-04-07T23:51:06","guid":{"rendered":"https:\/\/onlinemathtutor.co\/?page_id=21502"},"modified":"2022-05-28T20:46:48","modified_gmt":"2022-05-28T20:46:48","slug":"sequences-and-series-practice-problems-ratio-root-test","status":"publish","type":"page","link":"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-ratio-root-test\/","title":{"rendered":"Sequences and Series &#8211; Practice Problems \u2013 [Ratio &#038; Root Test]"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"21502\" class=\"elementor elementor-21502\" data-elementor-post-type=\"page\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6dca9ae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6dca9ae\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-597871eb\" data-id=\"597871eb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-68a5beab elementor-widget elementor-widget-heading\" data-id=\"68a5beab\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Practice Problems: Ratio Test and Root  Test<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-46769d9c elementor-nav-menu__align-center elementor-nav-menu--stretch elementor-nav-menu__text-align-center animated-fast elementor-nav-menu--dropdown-tablet elementor-nav-menu--toggle elementor-nav-menu--burger elementor-widget elementor-widget-nav-menu\" data-id=\"46769d9c\" data-element_type=\"widget\" data-settings=\"{&quot;submenu_icon&quot;:{&quot;value&quot;:&quot;&lt;i class=\\&quot;fas fa-pencil-alt\\&quot;&gt;&lt;\\\/i&gt;&quot;,&quot;library&quot;:&quot;fa-solid&quot;},&quot;full_width&quot;:&quot;stretch&quot;,&quot;_animation&quot;:&quot;none&quot;,&quot;layout&quot;:&quot;horizontal&quot;,&quot;toggle&quot;:&quot;burger&quot;}\" data-widget_type=\"nav-menu.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<nav aria-label=\"Menu\" class=\"elementor-nav-menu--main elementor-nav-menu__container elementor-nav-menu--layout-horizontal e--pointer-double-line e--animation-fast\">\n\t\t\t\t<ul id=\"menu-1-46769d9c\" class=\"elementor-nav-menu\"><li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-21593\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\">Sequences<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21590\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-sequences-limits\/\" class=\"elementor-sub-item\">Fundamentals &#038; Limits<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21769\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-pattern-recognition\/\" class=\"elementor-sub-item\">Pattern Recognition<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21902\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-pattern-recognition\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21768\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-monotonicity\/\" class=\"elementor-sub-item\">Monotonicity<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21904\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-monotonicity\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-21594\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\">Series Convergence Test<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21715\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-telescopic\/\" class=\"elementor-sub-item\">Telescopic Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21903\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-telescopic\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21716\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-geometric\/\" class=\"elementor-sub-item\">Geometric Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21899\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-geometric\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21717\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-dct-lct\/\" class=\"elementor-sub-item\">Direct Comparison Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21897\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-dct\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21718\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-lct\/\" class=\"elementor-sub-item\">Limit Comparison Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21898\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-lct\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21595\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-ratio-root-test\/\" class=\"elementor-sub-item\">Ratio Test &#038; Root Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21901\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-ratio-root-test\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21591\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-integral-test\/\" class=\"elementor-sub-item\">Integral Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21900\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-integral-test\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21596\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-alternating-series\/\" class=\"elementor-sub-item\">Alternating Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21896\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-alternating-series\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-21623\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\">Power Series<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21626\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-interval-of-convergence\/\" class=\"elementor-sub-item\">Interval of Convergence<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21892\"><a href=\"https:\/\/onlinemathtutor.co\/power-series-virtual-lessons-interval-of-convergence\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21624\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-taylor-polynomial\/\" class=\"elementor-sub-item\">Taylor Polynomial<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21894\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-taylor-polynomial\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21633\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-practice-problems-taylor-series\/\" class=\"elementor-sub-item\">Taylor Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21895\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-taylor-series\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21625\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-power-series-representation\/\" class=\"elementor-sub-item\">Power Series Representation<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21893\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-power-series-representation\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21627\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-applications-of-power-series\/\" class=\"elementor-sub-item\">Applications of Power Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21891\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-applications-of-power-series\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t<div class=\"elementor-menu-toggle\" role=\"button\" tabindex=\"0\" aria-label=\"Menu Toggle\" aria-expanded=\"false\">\n\t\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--open eicon-menu-bar\"><\/i><i aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--close eicon-close\"><\/i>\t\t<\/div>\n\t\t\t\t\t<nav class=\"elementor-nav-menu--dropdown elementor-nav-menu__container\" aria-hidden=\"true\">\n\t\t\t\t<ul id=\"menu-2-46769d9c\" class=\"elementor-nav-menu\"><li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-21593\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\" tabindex=\"-1\">Sequences<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21590\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-sequences-limits\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Fundamentals &#038; Limits<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21769\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-pattern-recognition\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Pattern Recognition<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21902\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-pattern-recognition\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21768\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-monotonicity\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Monotonicity<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21904\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-monotonicity\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-21594\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\" tabindex=\"-1\">Series Convergence Test<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21715\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-telescopic\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Telescopic Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21903\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-telescopic\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21716\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-geometric\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Geometric Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21899\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-geometric\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21717\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-dct-lct\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Direct Comparison Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21897\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-dct\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21718\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-lct\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Limit Comparison Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21898\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-lct\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21595\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-ratio-root-test\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Ratio Test &#038; Root Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21901\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-ratio-root-test\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21591\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-integral-test\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Integral Test<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21900\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-integral-test\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21596\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-alternating-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Alternating Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21896\"><a href=\"https:\/\/onlinemathtutor.co\/sequences-and-series-virtual-lessons-alternating-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-21623\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\" tabindex=\"-1\">Power Series<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21626\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-interval-of-convergence\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Interval of Convergence<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21892\"><a href=\"https:\/\/onlinemathtutor.co\/power-series-virtual-lessons-interval-of-convergence\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21624\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-taylor-polynomial\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Taylor Polynomial<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21894\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-taylor-polynomial\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21633\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-practice-problems-taylor-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Taylor Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21895\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-taylor-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21625\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-power-series-representation\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Power Series Representation<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21893\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-power-series-representation\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21627\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/sequences-and-series-practice-problems-applications-of-power-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Applications of Power Series<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21891\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/power-series-virtual-lessons-applications-of-power-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-30530751 elementor-section-stretched elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"30530751\" data-element_type=\"section\" data-settings=\"{&quot;stretch_section&quot;:&quot;section-stretched&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-14539151\" data-id=\"14539151\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-72e666c0 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"72e666c0\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-59203b41 elementor-widget elementor-widget-text-editor\" data-id=\"59203b41\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: center;\"><span style=\"font-size: 18px;\">[INFO ON THESE TYPES OF SERIES]<\/span><\/p><p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">The main objective of determining if a given series converges or diverges is to answer the questions of Yes or No. <strong><a href=\"https:\/\/onlinemathtutor.co\/index.php\/course-content\/integration\/integration-formulas-update\/\" target=\"_blank\" rel=\"noopener\">See Convergence Test<\/a><\/strong>.\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3c6d6ecf elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"3c6d6ecf\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div 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data-id=\"401f8242\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-59acf644 elementor-view-framed elementor-position-left elementor-shape-circle elementor-mobile-position-top elementor-vertical-align-top elementor-widget elementor-widget-icon-box\" data-id=\"59acf644\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<a href=\"https:\/\/onlinemathtutor.co\/index.php\/sequences-and-series-virtual-lessons-ratio-root-test\/?playlist=149217f3&#038;video=4caefd9\" class=\"elementor-icon elementor-animation-grow\" tabindex=\"-1\" aria-label=\"Virtual Lessons\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"fas 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Click Here to visit the virtual lesson section. \t\t\t\t\t<\/p>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-75c458f\" data-id=\"75c458f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-58dc66c7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"58dc66c7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4b63c21f\" data-id=\"4b63c21f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d696908 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"d696908\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51a82213 elementor-widget elementor-widget-spacer\" data-id=\"51a82213\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7ac722eb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7ac722eb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3e3b5fe8\" data-id=\"3e3b5fe8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-575aad99 elementor-widget elementor-widget-heading\" data-id=\"575aad99\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-large\">Practice Problems<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3c65a3db elementor-widget elementor-widget-text-editor\" data-id=\"3c65a3db\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: justify;\"><span style=\"font-size: 18px;\">Determine whether the given <strong>telescopic series<\/strong> converges or diverges. If a series converges then compute its sum.\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-55a9e0eb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"55a9e0eb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5bc6677b\" data-id=\"5bc6677b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-723e53b6 elementor-widget elementor-widget-text-editor\" data-id=\"723e53b6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol start=\"1\"><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}\\left(\\frac{1}{n}-\\frac{1}{n+1}\\right)\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\displaystyle \\sum_{n=0}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n \\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n \\)<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-7fecbe55\" data-id=\"7fecbe55\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3a6d5233 elementor-widget elementor-widget-text-editor\" data-id=\"3a6d5233\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol start=\"6\"><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\displaystyle \\sum_{n=0}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n \\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n \\)<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-7f851053\" data-id=\"7f851053\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1253e11b elementor-widget elementor-widget-text-editor\" data-id=\"1253e11b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ol start=\"11\"><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\displaystyle \\sum_{n=0}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n \\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n\\)<\/li><li style=\"margin-bottom: 30px;\">\\(\\displaystyle \\sum_{n=1}^{\\infty}a_n \\)<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-51d248f0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"51d248f0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-441de896\" data-id=\"441de896\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5a06d34e elementor-align-left elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"5a06d34e\" data-element_type=\"widget\" data-widget_type=\"icon-list.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/onlinemathtutor.co\/index.php\/problem-set-sequences-series\/\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-arrow-circle-right\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Back To Main Page: Sequences and Series Problem Sets<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3edbcf90 elementor-widget elementor-widget-spacer\" data-id=\"3edbcf90\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-12a8ed83 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"12a8ed83\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7ab276a2\" data-id=\"7ab276a2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-936f141 elementor-widget elementor-widget-heading\" data-id=\"936f141\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-large\">Suggestive Solution Guide<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-13e82aba elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"13e82aba\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-32e63118\" data-id=\"32e63118\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2bed5d5 elementor-widget elementor-widget-toggle\" data-id=\"2bed5d5\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-4601\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-4601\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 1: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-4601\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-4601\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 1: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7224fb80 elementor-widget elementor-widget-toggle\" data-id=\"7224fb80\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-1911\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1911\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 2: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1911\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1911\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 2: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-24ff9054 elementor-widget elementor-widget-toggle\" data-id=\"24ff9054\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-6201\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-6201\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 3: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-6201\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-6201\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 3: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-63a9be99 elementor-widget elementor-widget-toggle\" data-id=\"63a9be99\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-1671\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1671\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 4: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1671\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1671\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 4: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e1f9702 elementor-widget elementor-widget-toggle\" data-id=\"e1f9702\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-2361\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2361\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 5: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2361\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2361\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 5: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ce1857b elementor-widget elementor-widget-toggle\" data-id=\"ce1857b\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-2161\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2161\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 6: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2161\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2161\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 6: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-64475ffa elementor-widget elementor-widget-toggle\" data-id=\"64475ffa\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-1681\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1681\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 7: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1681\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1681\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 7: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6e654d15 elementor-widget elementor-widget-toggle\" data-id=\"6e654d15\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-1851\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1851\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 8: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1851\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1851\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 8: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4669adcf elementor-widget elementor-widget-toggle\" data-id=\"4669adcf\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-1181\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1181\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 9: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1181\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1181\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 9: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7a55f3f2 elementor-widget elementor-widget-toggle\" data-id=\"7a55f3f2\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-2051\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2051\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 10: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2051\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2051\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 10: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6684eb29 elementor-widget elementor-widget-toggle\" data-id=\"6684eb29\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-1711\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1711\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 11: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1711\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1711\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 11: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-552f092b elementor-widget elementor-widget-toggle\" data-id=\"552f092b\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-1421\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1421\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 12: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1421\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1421\"><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Problem 12: Solution\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c372586 elementor-widget elementor-widget-toggle\" data-id=\"c372586\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<h2 id=\"elementor-tab-title-2041\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2041\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-toggle-off\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-toggle-on\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Problem 13: Solution<\/a>\n\t\t\t\t\t<\/h2>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2041\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" 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Equations<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21606\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/parametric-equations-2\/problem-set-parametric-eqs-2\/\" class=\"elementor-sub-item\"><img decoding=\"async\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2022\/02\/Problem-Sets.png\"  width=\"20\" style=\"margin-right: 10px;\">  Problem Set<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-12615\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/parametric-equations-2\/virtual-lessons-parametric-equations\/\" class=\"elementor-sub-item\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-10232\"><a 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Rule<\/a><\/li>\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-10229\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/differentiation\/differentiation-applications\/curve-analysis\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Curve Analysis<\/a><\/li>\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-11435\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/differentiation\/differentiation-applications\/related-rates\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Related Rates<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-20868\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/differentiation\/problem-set-differentiation\/\" class=\"elementor-sub-item\" tabindex=\"-1\"><img decoding=\"async\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2022\/02\/Problem-Sets.png\"  width=\"20\" style=\"margin-right: 10px;\">  Problem Set<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-14329\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\" tabindex=\"-1\">Integration<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-14551\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/integration\/fundamentals-integration\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Fundamentals<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-10226\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/integration\/riemann-sums\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Riemann Sums<\/a><\/li>\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-11365\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/integration\/fundamental-theorem-of-calculus\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Fundamental Theorem of Calculus<\/a><\/li>\n\t<\/ul>\n<\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-11530\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/integration\/integration-formulas-update\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Integration Formulas<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-9815\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/integration\/integration-techinques\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Integration Techinques<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-13700\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/integration\/integration-applications\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Integration Applications<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-19550\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/integration\/problem-set-integration\/\" class=\"elementor-sub-item\" tabindex=\"-1\"><img decoding=\"async\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2022\/02\/Problem-Sets.png\"  width=\"20\" style=\"margin-right: 10px;\">  Problem Set<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-14330\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\" tabindex=\"-1\">Sequences and Series<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-11364\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Fundamentals<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-9804\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/convergence-test\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Convergence Test<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-10233\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/power-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Power Series<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-11363\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/taylor-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Taylor Series<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-21607\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/problem-set-sequences-series\/\" class=\"elementor-sub-item\" tabindex=\"-1\"><img decoding=\"async\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2022\/02\/Problem-Sets.png\"  width=\"20\" style=\"margin-right: 10px;\">  Problem Set<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children menu-item-14331\"><a href=\"#\" class=\"elementor-item elementor-item-anchor\" tabindex=\"-1\">Parametric Equations<\/a>\n<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-12174\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/parametric-equations-2\/fundamentals-of-parametric-equations\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Fundamentals<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-19376\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/parametric-equations-2\/polar-coordinates-calculus\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Polar Coordinates<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-11366\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/precalculus-resources\/unit-circle\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Unit Circle<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-12198\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/parametric-equations-2\/calculus-parametric-equation\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Calculus of Parametric Equations<\/a><\/li>\n\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children menu-item-21606\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/parametric-equations-2\/problem-set-parametric-eqs-2\/\" class=\"elementor-sub-item\" tabindex=\"-1\"><img decoding=\"async\" src=\"https:\/\/onlinemathtutor.co\/wp-content\/uploads\/2022\/02\/Problem-Sets.png\"  width=\"20\" style=\"margin-right: 10px;\">  Problem Set<\/a>\n\t<ul class=\"sub-menu elementor-nav-menu--dropdown\">\n\t\t<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-12615\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/parametric-equations-2\/virtual-lessons-parametric-equations\/\" class=\"elementor-sub-item\" tabindex=\"-1\">Virtual Lessons<\/a><\/li>\n\t<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-10232\"><a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/ap-calculus-frqs\/\" class=\"elementor-item\" tabindex=\"-1\">AP Calculus Prep<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0c4c756\" data-id=\"0c4c756\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f6e1e21 elementor-widget elementor-widget-spacer\" data-id=\"f6e1e21\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Practice Problems: Ratio Test and Root Test [INFO ON THESE TYPES OF SERIES] The main objective of determining if a given series converges or diverges is to answer the questions of Yes or No. See Convergence Test.\u00a0 Virtual Lessons Need <a href=\"https:\/\/onlinemathtutor.co\/course-content\/calculus-resources\/sequences\/sequences-and-series-practice-problems-ratio-root-test\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":11339,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"class_list":["post-21502","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Sequences and Series - Practice Problems \u2013 [Ratio &amp; Root Test] | Online Math Tutoring LLC | Expert Math Tutor Near Me<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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