# Thread: Proving convergence of divergence of a series.

1. ## Proving convergence of divergence of a series.

Thanks for the help... there is one more that I can't get.

$\sum_{n=1}^{\infty} \frac{n}{n \sqrt{n} + 2}$

I just have trouble seeing how to prove they converge or diverge. I guess I just need to practicing them!

2. Originally Posted by Benno_11
Thanks for the help... there is one more that I can't get.

$\sum_{n=1}^{\infty} \frac{n}{n \sqrt{n} + 2}$

I just have trouble seeing how to prove they converge or diverge. I guess I just need to practicing them!
Note that $\frac{n}{n \sqrt{n} + 2} > \frac{n}{n \sqrt{n} + n \sqrt{n}}$ for $n > 1$. Now use the comparison test.