17 questions linked to/from Prove by induction that $n^2<n!$
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### Hint in Proving that $n^2\le n!$ [duplicate]

The problem is to find the values of n such $n^2\le n!$. I have found this set to be {${n\in Z^+| n\le1 \lor n\ge 4}$} I've used a proof by cases to prove the first part ($\forall n\le 1$) which was ...
### Prove by induction that $n! > n^2$ [duplicate]
How does one prove by induction that $n! > n^2$ for $n \geq 4$