Solution: Alternating Series Test Determine whether the

Chapter 10, Problem 16E

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QUESTION:

11-24. Alternating Series Test Determine whether the following series converge.

\(\sum_{k=0}^{\infty}\left(-\frac{1}{5}\right)^{k}\)

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QUESTION:

11-24. Alternating Series Test Determine whether the following series converge.

\(\sum_{k=0}^{\infty}\left(-\frac{1}{5}\right)^{k}\)

ANSWER:

Problem 16E

Alternating Series Test
Determine whether the following series converge.

Solution:
Step 1
Consider the general form of alternating series:

Alternating Series test says that if decreases monotonically and then the alternating series converges.

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