I have to prove that $\displaystyle 2^n < n! for all n>4 $ using induction.

So,um I started like this,

$\displaystyle p(n) : 2^n < n !$

so $\displaystyle p(n+1) : 2^(n+1) < (n+1)!$

=> $\displaystyle 2^n * 2 < (n+1) * n!$

=> $\displaystyle 2^n < (n+1)/2 * n!

$

so um idk what to do next.How do I prove that this prove holds for all n>4