TITLE: Squeeze Theorem with Factorial
QUESTION [5 upvotes]: 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.

REPLY [7 votes]: 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.