test for convergence/divergence of the series $\displaystyle \sum_{n =1}^{\infty}\frac{e^{1/n}}{n^2}$
i'm just wondering if i should use the integral test here..or if it can just be compared to the p series (p=2)
Direct comp, since $\displaystyle e^{1/n}\to 1 $ as $\displaystyle n\to\infty$
use $\displaystyle 0<e^{1/n}<100$ so $\displaystyle \sum_{n =1}^{\infty}\frac{e^{1/n}}{n^2} < 100\sum_{n =1}^{\infty}\frac{1}{n^2}<\infty$
where the 100 is larger than what you need, but it get the point across.
The max of $\displaystyle e^{1/n}$ is actually $\displaystyle e$. So, any number $\displaystyle e$ or larger works, but that's not important.