Hi I am supposed to determine if the following series converges or diverges. The catch is that we are only allowed to use the comparison test, ratio test, and root test.

First one is

$\displaystyle \sum[\sqrt{n+1}-\sqrt{n}]$

and 2nd one is

$\displaystyle \sum\frac{n!}{n^n}$

any hints or the full blown solution would be great.