I need some help with this problem.
Need to prove:
2^{n-1} <= n! for n >= 1
Not sure where to start. Any clues or push in the right direction would be appreciated.
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?