## Calculus (3rd Edition)

$0$.
We have $$\lim _{n \rightarrow \infty} a_n=\lim _{n \rightarrow \infty}\frac{10^n}{n!}=0.$$ Since we know that for all $n\gt \gt 10$, $n!$ is getting bigger faster than $10^n$. Hence, $a_n$ converges to $0$.