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Practice Problems: Sequence Fundamentals & Limits

[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.

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Practice Problems

Determine whether the given telescopic series converges or diverges. If a series converges then compute its sum.

\(\displaystyle \sum_{n=1}^{\infty}\left(\frac{1}{n}-\frac{1}{n+1}\right)\)
\(\displaystyle \displaystyle \sum_{n=0}^{\infty}a_n\)
\(\displaystyle \sum_{n=1}^{\infty}a_n \)
\(\displaystyle \sum_{n=1}^{\infty}a_n\)
\(\displaystyle \sum_{n=1}^{\infty}a_n \)

\(\displaystyle \sum_{n=1}^{\infty}a_n\)
\(\displaystyle \displaystyle \sum_{n=0}^{\infty}a_n\)
\(\displaystyle \sum_{n=1}^{\infty}a_n \)
\(\displaystyle \sum_{n=1}^{\infty}a_n\)
\(\displaystyle \sum_{n=1}^{\infty}a_n \)

\(\displaystyle \sum_{n=1}^{\infty}a_n\)
\(\displaystyle \displaystyle \sum_{n=0}^{\infty}a_n\)
\(\displaystyle \sum_{n=1}^{\infty}a_n \)
\(\displaystyle \sum_{n=1}^{\infty}a_n\)
\(\displaystyle \sum_{n=1}^{\infty}a_n \)

Suggestive Solution Guide

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Problem 5: Solution

Problem 6: Solution

Problem 7: Solution

Problem 8: Solution

Problem 9: Solution

Problem 10: Solution

Problem 11: Solution

Problem 12: Solution

Problem 13: Solution

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