Prove that n! > n2 for every integer n ≥ 4, whereas n! > n3 for every integer n ≥ 6.
The Attempt at a Solution
Ok, I am attempting an induction proof, but I seem to be stuck in the following step. In any case, I don't even know if what I have is correct. I'm skipping over n=1 and n=k.
for n = k+1
(k+1)! = k!(k+1)
k!(k+1) > (k+1)2
I don't know what to do next or even if I'm on the right path.
I think if I can get help with this first part I might be able to solve the second part (n! > n3).