Assume that K>4 and that we know that (K!)>2^K.
Look at (K+1)!=(K+1)(K!) !)>(K+1)2^K>(4)2^K>2^(K+1)
Prove that n! > 2^n for every integer n greather than or equal to 4.
This is what I have so far.
Proof: Since 4! > 2^4 the statement is true for n greater than or equal to 4. Assume k!>2^k for some positive integer k. Observe: (k+1)! > 2^(k+1).
I am doing okay with math induction with equal signs and not greater or less than signs. Can any one help?