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.

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- Feb 27th 2013, 07:47 PMsreckerInductive proof help
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. - Feb 27th 2013, 10:55 PMsreckerRe: Inductive proof help
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?