# Homework Help: Series Convergence

1. Apr 17, 2014

### analysis001

1. The problem statement, all variables and given/known data
Prove that the series $\sum_{n=1}^{\infty}\frac{\sqrt{n+1}-\sqrt{n}}{n}$ converges.

3. The attempt at a solution
I think I'm going to use the comparison test but I'm having trouble coming up with a series to compare it to. Any clues would be great. Thanks!

2. Apr 17, 2014

### SammyS

Staff Emeritus
Try rationalizing the numerator.

3. Apr 17, 2014

### analysis001

Yeah, I've gotten to that point, so as of now I have: $\sum_{n=1}^{\infty}\frac{1}{n(\sqrt{n+1}+\sqrt{n})}$ but I'm still not sure what to compare it to.

4. Apr 17, 2014

### SammyS

Staff Emeritus
Let's see ...

$\sqrt{n+1}\ \ > \sqrt{n}$

How can that help ?