How do i use induction(effectively) to prove that n! < nn for n ≥ 2 ?

let p(n): n! < nn for n ≥ 2.

we see that p(2) holds true.

now i prove it holds for p(n+1) right?

(n+1)! = (n+1)n!<(n+1)nn by the induction hypothesis.

i think this is right.. can someone show me how to finish this correctly?

thanks

Kyle