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Practice Problems: Sequence Pattern Recognition

[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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Need some additional help understanding how to approach these types of seqeunces? Click Here to visit the virtual lesson section.

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

Problem 1: Solution

Problem 2: Solution

Problem 3: Solution

Problem 4: Solution

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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