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## Homework Statement

Prove that n! > n

^{2}for every integer n ≥ 4, whereas n! > n

^{3}for every integer n ≥ 6.

## Homework Equations

See above.

## 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! > n

^{3}).