Answer
Converges
Work Step by Step
Apply the Ratio test to the series
$\Sigma^{\infty}_{n=1} \frac{1}{n!}$
$\lim\limits_{n \to \infty} |\frac{\frac{1}{(n+1)!}}{\frac{1}{n!}}|$
$\lim\limits_{n \to \infty} |\frac{n!}{(n+1)!}|$
$\lim\limits_{n \to \infty} \frac{1}{n+1} = 0 \lt 1$
Because the answer is less than 1, the series converges
