Answer
Diverges
Work Step by Step
Apply the ratio test to the Series
$\Sigma^{\infty}_{n=0} \frac{n!}{3^n} $
$\lim\limits_{n \to \infty} |\frac{\frac{(n+1)!}{3^{n+1}}}{\frac{n!}{3^n}}|$, Simplify
$\lim\limits_{n \to \infty} \frac{(n+1)}{3} = \infty \gt 1$
Because the answer is greater than 1, the series diverges.
