# Prove the inequality $n! > 2^n$ by induction. [duplicate]

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.