Squeeze Theorem with Factorial

Question

Is it correct to squeeze $\frac{3n}{(n+1)!}$ between $0$ and $\frac{1}{n!}$? The proposed left side makes logical sense to me, however bounding the right hand side to prove the limit goes to $0$ is giving me a bit more trouble.

Answer 1

Note that since $n<n+1$, one have that $$ 0\le \frac{3n}{(n+1)!} \le \frac{3}{n!}$$ Using Squeeze Theorem, it can be easily seen that the limit is zero.