Determine the result of
$\lim\limits_{n\to\infty}\frac{n^{n+1}}{n!}.$
I would like to use the sandwich rule for limits to find two sequences which define lower and upper bounds to determine the appropriate limit which is obviously $+\infty$.
By now I have an upper bound:
$\frac{n^{n+1}}{n!}=n\cdot\frac{n}{n}\cdot\frac{n}{n-1}\cdot\ldots\cdot\frac{n}{2}\cdot\frac{n}{1}\leq n\cdot 1\cdot n\cdot\ldots\cdot n\cdot n=n^n\longrightarrow+\infty$
What would you suggest, which sequence should I use for a lower bound which converges to $+\infty$?