1. The problem statement, all variables and given/known data For all integers n=>1, n! <= n^n 2. Relevant equations 3. The attempt at a solution Let p(n) be the inequality n! <= n^n, for all integers n=>1. Base case: p(1) = 1! <=1^1 1<=1 check IHOP: Assume p(k), that is assume k!<=k^k for some integer k. Show p(k+1): show (k+1)! <= (k+1)^(k+1) It can be rewritten as k!(k+1) <= (k+1)^k (k+1) divide both sides by (k+1) which leaves k! <= (k+1)^k Is this correct or so I beg the question/ mess up my simple math?