Answer
Diverges
Work Step by Step
In order to solve the given series we will take the help of Ratio Test. This test states that when the limit $L \lt 1$, the series converges and for $L \gt 1$, the series diverges.
Let us consider $a_n=\dfrac{n! }{10^n}$
$L=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{(n+1)! }{10^{(n+1)}}}{\dfrac{n!}{10^{(n)}}}|$
$\implies (\dfrac{1}{10})\lim\limits_{n \to \infty}(n+1)=(\dfrac{1}{10})(\infty)=\infty \gt 1$
Hence, the series Diverges by the ratio test.