OK, I think may have figured this out.

I am not very good at this, here it is.

Prove: 2^{n-1}<= n! for n >= 1

If we assume that P(k): 2^{k-1}<= n! for some integer k and k >= 1

then need to prove that 2^{k}<= (k+1)!

therefore 2^{k}=2*2^{k-1}<=2k! <= (k+1)k! = (k+1)!

I think this is it, but I'm not sure.

Comments?