(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\sum_{n=1}^{\infty}(-1)^{n+1}\frac{\sqrt{n}+1}{n+1}[/tex]

2. Relevant equations

absolute convergence test

3. The attempt at a solution

by book says that the series converges because [tex]\sum_{n=1}^{\infty}\frac{\sqrt{n}+1}{n+1}[/tex] converges

but they dont show how the absolute value of the original series converges, and ive tried showing it myself but i keep getting divergence

i know that as n grows larger and larger the behavior of [tex]\frac{\sqrt{n}+1}{n+1}[/tex] is similar to that of [tex]\frac{\sqrt{n}}{n}[/tex] so i tried using limit comparison and direct comparison with [itex]\frac{1}{n}[/itex] but i keep getting divergence

i tried the integral test but i kept getting divergence also

ive been trying this for far too long so any help would be greatly appreciated

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# Homework Help: Absolute convergence help

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