Answer
Converges
Work Step by Step
Given
$$\sum_{n=1}^{\infty} \frac{e^n}{n! }$$
By using the Ratio Test, we get:
\begin{align*}
\rho&=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|\\
&=\lim _{n \rightarrow \infty} \frac{e^{n+1}}{(n+1)! }\frac{n! }{e^n} \\
&= \lim _{n \rightarrow \infty} \frac{e}{n+1}\\
&= 0<1
\end{align*}
Thus the series converges.
