Answer
Converges
Work Step by Step
Consider $a_n=\dfrac{n!}{n^n}$
Now, $l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{(n+1)!}{(n+1)^{n+1}}}{\dfrac{n!}{n^n}}|$
Thus, we have $l=\lim\limits_{n \to \infty}|(\dfrac{n^n (n+1)}{(n+1)^n(n+1)})|=\lim\limits_{n \to \infty}|(1-\dfrac{1}{n+1)})^n|=\lim\limits_{n \to \infty}|\dfrac{(1-\dfrac{1}{n+1)})^{n+1}}{(1-\dfrac{1}{n+1)})^n}|$
So, $l=\dfrac{e^{-1}}{1}=\dfrac{1}{e} \lt 1$
Hence, the series Converges by the ratio test.