Show that $\displaystyle e^n>\frac{(n+1)^n}{n!}$ where n is an integer
boy, do I suck at this stuff.
This cant be done by induction?
It holds for n = 1.
Assume it holds for n=k, prove it holds for n=k+1.
$\displaystyle e^{k+1}=e^{k}\cdot e > \frac{(k+1)^{k}}{k!} \cdot e $
I´m not saying this is correct at all, just giving some thoughts! =)