Mathematical induction

So I have to prove, by mathematical induction, that 2^n <= n! for every positive integer where n >= 4.

However, while I do understand the basics of induction, I haven't a clue how to work with factorial numbers.

Any (preferably elaborate) tips? :3

Sorry, I made a mistake. It's supposed to be n^2 <= n!, not 2^n, which for some reason, would make my life so much easier :/

Actually, I think this proof is easier with 2^n than with n^2.

n^2 <== n! for n = 4 (16<= 24)
Then assume n^2 <= n! for n = k
(k+1)^2 = k^2 + 2k +1 =< k! + 2k + 1 =< k! +k*k! (I'm sure you can justify this yourself) = (k+1)!

so it follows

That's what I meant. I can do it fairly easy for 2^n, but am having trouble doing it for n^2.

>>4
I have no clue how you got your "k! +2k +1" into that.

>>6
(Not >>4)
The assumption (by induction) is that k^2 =< k!. Therefore, k^2 + 2k + 1 =< k! + 2k + 1.