hello people!

in this question it says prove the following using mathematical induction:

n! < n^n

p(2) = 2! < 2^2 (True)

p(n) = n! < n^n

p(n+1) = (n+1)! < n ^ (n+1)

proof:

n . n! < n^n . n

n. n! < n ^ (n+1)

(n+1).n! < n^ (n+1)

(n+1)! < n ^ (n+1)

is this true??? I dont think so ....

Thanks in advance for helping me