Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 716: 42

Divergent

$a_{n}=\frac{e^{n}}{n^{2}}$ $\lim\limits_{n \to \infty} a_{n} = \lim\limits_{n \to \infty}\frac{e^{n}}{n^{2}}$ Use L'hospital's rule $=\lim\limits_{n \to \infty} \frac{e^{n}}{2n}$ $=\lim\limits_{n \to \infty} \frac{e^{n}}{2}$ $=\infty$ $\ne 0$ Therefore the series is divergent.