Answer: Consider the following series. (a) Does the series meet the conditions of
Chapter 9, Problem 86(choose chapter or problem)
Consider the following series.
\(\sum_{n=1}^{\infty}(-1)^{n+1} \ a_{n}, \ a_{n}=\left\{\begin{array}{ll} \frac{1}{\sqrt{n}}, & \text { if } n \text { is odd } \\ \frac{1}{n^{3}}, & \text { if } n \text { is even } \end{array}\right.\)
(a) Does the series meet the conditions of Theorem 9.14? Explain why or why not.
(b) Does the series converge? If so, what is the sum?
Text Transcription:
sum_n=1 ^infty (-1)^n+1 a_n, a_n = { _1/n^3, if n is even ^1/sqrt n, if n is odd
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