Proving by induction that $n^{n+1} > (n+1)^n$ for $n \ge 3$

Question

Prove the following inequality by mathematical induction:

$$n^{n+1}>{(n+1)}^n \qquad (n\geq3)$$

Obviously it holds for $n=3$.

Assume $P(n)$ holds, then $LHS=n^{n+1}$