Answer
Diverges
Work Step by Step
Consider the series $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n^n}{n!}$ = $\lim\limits_{n \to \infty} \dfrac{(n)(n).....(n) }{ (1)(2)....(n)} $
We can see that the numerator will be increasing more than the terms in the denominator.
$\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n^n}{n!}=\infty \ne 0$
Hence, the given series diverges.