then by dividing RHS ==>

n^(n+1) / (n+1)^n > 1 ==>

n * n^n / (n+1)^n > 1 ==>

n * [ n/(n+1)]^n > 1 ==>

n * [1/(1+1/n)]^n > 1 ==>

n / (1 + 1/n)^n > 1

and for n > 2, then (1+1/n) < 2

so it is true that n / (1 + 1/n)^n > 1

Working backwards with this last fact, you find that n^(n+1) > (n+1)^n