Proof by induction: $n! > n^2$ for $n\ge 4$ Proof by induction: $n! > n^2$ for $n\ge 4$
Basis step:
if $n=4$
$4\cdot3\cdot2\cdot1 > 4^2$
$24 > 16$
I don't know how to do the inductive step.

Inductive step
Assume it holds for $k$
$$k!\gt k^2 \implies (k+1)! \gt (k+1)k^2 \gt (k+1)(k+1)=(k+1)^2$$
