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Alternating Series Test Determine whether the
Chapter 10, Problem 24E(choose chapter or problem)
QUESTION:
11-24. Alternating Series Test Determine whether the following series converge.
\(\sum_{k=1}^{\infty}(-1)^k\ k\sin\left(\frac{1}{k}\right)\)
Questions & Answers
QUESTION:
11-24. Alternating Series Test Determine whether the following series converge.
\(\sum_{k=1}^{\infty}(-1)^k\ k\sin\left(\frac{1}{k}\right)\)
ANSWER:Problem 24E
Alternating Series Test Determine whether the following series converge.
Solution
Step 1
In this problem we have to find whether the series converge or not.
Alternating series test:
Suppose that for there exists a N so that for all
- is positive and decreasing
- .