Answer
TRUE
Work Step by Step
Ratio Test:
$\lim\limits_{n \to +\infty}|\frac{a_{n}+1}{a_{n}}|=\lim\limits_{n \to +\infty}|\frac{1}{n+1!}\times \frac{n!}{1}|$
Here, $\frac{1}{n+1!}$ can also written as
$\frac{1}{n+1!}=\frac{1}{n!}\times \frac{1}{n+1}$
Therefore,
$\lim\limits_{n \to +\infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to +\infty}|\frac{1}{n+1}|=0$
So, the given series converges by Ratio Test when limit equals $0$ which is $\lt 1$ .
Hence, the statement is TRUE.
