Possible Duplicate:
Proof the inequality $n! \geq 2^n$ by induction
Prove By Induction that $n!>2^n$
I have to prove the inequality $n! > 2^n$ for all integers $n \geq4$.
I am having trouble with this.
I am assuming that: $n! > 2^n \implies (n+1)! > 2^{n+1}$.
I have proven the base case is true, as $4! > 2^4$.
For the induction step, I get: $(n+1)! = (n+1)n!$
After that, I am not sure what to do.
Thanks.