- #1

miglo

- 98

- 0

## Homework Statement

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

## Homework Equations

absolute convergence test

## 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 don't show how the absolute value of the original series converges, and I've 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