1. ## Does this converge?

Does the series converge or diverge? If it converges find the sum.

2. $\sum_{n=1}^{\infty} {ne^{-n^2}}$

use the integral test to show convergence ... have to think about the actual sum.

3. Even better, $\sqrt[n]{{ne^{ - n^2 } }} = \frac{{\sqrt[n]{n}}}
{{e^n }}$