I am trying to prove the inequality in the title for $n\geq 4$; however, I am stuck on the induction step! Any help would be appreciated.
For $n\ge 4$, prove that $n! > n^2$.
Base Case: $n=4$, LHS $4! = 24$, RHS = $4^2 = 16$
$24>16$ : True
Induction Hypothesis: Assume True for $n=k$.
$k! > k^2$
Induction Step: Should be True for $n=k+1$
$(k+1)! > (k+1)^2$
$(k+1) . (k)! > (k^2 + 2k + 1)$
However, here is where I get stuck.