$\displaystyle \sum_{n=1}^\infty \frac{\sqrt{2n^3+n^2-6}}{4n\sqrt{n}+4}$

$\displaystyle \sum_{n=1}^\infty \frac{1}{\sqrt{n^3}e^n}$

The problem is to decide if the series converge or diverge. I have tried the n-th term and integral tests but to no avail.

For the second problem, I have shown that the n-th term test does not diverge, but that does not nececarily show that it DOES converge, I believe.