Answer
$0$
Work Step by Step
We are given the sequence:
$\left\{\dfrac{3^n}{n!}\right\}$
Let $a_n=3^n$ and $b_n=n!$.
As $3^n\ll n!$, we have: $a_n\ll b_n$. Because $a_n$ appears before $b_n$ in the list of growth rates, using Theorem 8.6, we get:
$\lim\limits_{n \to \infty} \dfrac{a_n}{b_n}=0$
