How to prove $n!>(\frac{n}{e})^{n}$

How to prove $n!>(\frac{n}{e})^{n}$

Prove that $n!>\left(\dfrac{n}{e}\right)^{n}$.
I used induction principle but cannot solve it for the $(m+1)$-th term
after taking the $m$th term to be true.