Answer
Divergent
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{n!}{10^{6n}}$
Since, $\lim\limits_{n \to \infty} \dfrac{x^n}{n!}=0$ when $x \gt 0$
So, $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{n!}{10^{6n}}= \lim\limits_{n \to \infty} \dfrac{1}{\dfrac{(10^{6})^n}{n!}}=\dfrac{1}{0}=\infty$
Hence, $\lim\limits_{n \to \infty} a_n=\infty$ and {$a_n$} is Divergent
