Answer
diverges.
Work Step by Step
To find whether the sequence converges, take the limit as $n$ approaches infinity.
$\lim\limits_{n \to \infty} \frac {(n+1)!}{n!}$
Change the $(n+1)!$ to $(n+1)\times(n)!$. Therefore,
$\lim\limits_{n \to \infty} \frac {n!(n+1)}{n!}$
$=\lim\limits_{n \to \infty} {n+1}=\infty$; limit doesn't exists; therefore, the sequence diverges.
