Answer
Diverges
Work Step by Step
In order to solve the given series we will take the help of Ratio Test. This test states that when the limit $L \lt 1$, the series converges and for $L \gt 1$, the series diverges.
Let us consider $a_n=(n!) (e^{-(n)})$
$L=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{(n+1)! e^{-(n+1)}}{(n!) e^{-n}}|$
$\implies (\dfrac{1}{e})\lim\limits_{n \to \infty}(n+1)=(\dfrac{1}{e})(\infty)=\infty \gt 1$
Hence, the series Diverges by the ratio test.