Math induction ($n^2 \leq n!$) help please I'm having trouble with a math induction problem.  I've been doing other proofs (summations of the integers etc) but I just can't seem to get my head around this.

Q.  Prove using induction that $n^2 \leq n!$

So, assume that $P(k)$ is true: $k^2 \leq k!$
Prove that $P(k+1)$ is true: $(k+1)^2 \leq (k+1)!$
I know that $(k+1)! = (k+1)k!$ so:  $(k+1)^2 \leq (k+1)k!$  but where can I go from here?
Any help would be much appreciated.

Suppose $k^{2}\leq k!$. Then $(k+1)!=(k+1)k!\geq (k+1)k^{2}\geq (k+1)^{2}$, whenever $k\geq 2$.
