I let somebody else do this problem. It is just boring.

We see that,2) The number n!, which is the number of permutations of the first n positive integers, is defined recursively by 0! = 1 and n! = n X (n-1)! for all n > o. Prove that n! < n ^n for all n > 0 and strict inequality holds if n > 1.

Good.

Next there is a such as,

But,

Multiply by both sides by

Thus,

Q.E.D.