How to prove by method of induction a statement with factorials

Question

The question:

Prove that for all positive integers $n \geq 4$, $2^{n} < n!$

The base case is fine, but how do you proceed with inductive step?

$(2^{k} < k!) \implies ( 2^{k+1} < (k+1)!)$

Answer 1

Intuitively, to go from $n!$ to $(n+1)!$ you multiply by $n+1$, which is greater than $2$.