(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that n! > n^{2}for every integer n ≥ 4, whereas n! > n^{3}for every integer n ≥ 6.

2. Relevant equations

See above.

3. 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}).

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Induction proof n! > n^2

**Physics Forums | Science Articles, Homework Help, Discussion**