Show that if $n ≥ 6$, then $n! > n^3$
Initial Step: $n = 6$
LHS: $6!=720$ RHS: $6^3=216$ LHS > RHS
Inductive Step: Assume $n=k$ is true
$k! > k^3$
Prove $n=k+1$ is true
$(k+1)! > (k+1)^3$
Can you help me? I don't know where to go from here. I'm stuck in here.