Answered: 00 (-1)"+1 Is En=1 convergent…

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00 (-1)"+1 Is En=1 convergent absolutely, non-absolutely, or diverges. n+8

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 16E

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Question

Is £
(-1)"+1
convergent absolutely, non-absolutely, or diverges.
Zn=1
n+8

Expert Solution

Step 1

Given series is

$\sum_{n = 1}^{\infty} \frac{{(- 1)}^{n + 1}}{n + 8}$

Absolute convergent test: If $\sum |a_{n}|$ converges, then $\sum a_{n}$ converges.

Let $a_{n} = \frac{{(- 1)}^{n + 1}}{n + 8}$ , then

$|a_{n}| = \frac{1}{n + 8}$

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