Answer
Divergent
Work Step by Step
As we know that a sequence converges when $\lim\limits_{n \to \infty}a_n$ exists.
Consider $a_n= \dfrac{(n+1)!}{n!}$
or, $a_n= \dfrac{n!(n+1)}{n!}=(n+1)$
Apply limits to both sides.
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty} (n+1)$
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}n+\lim\limits_{n \to \infty}(1)$
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty} (n+1)=\infty$
Hence, the sequence is divergent.
