Prove by induction that $n!>2^n$ 
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Proof the inequality $n! \geq 2^n$ by induction  

Prove by induction that $n!>2^n$ for all integers $n\ge4$.
I know that I have to start from the basic step, which is to confirm the above for $n=4$, being $4!>2^4$, which equals to $24>16$.
How do I continue though. I do not know how to develop the next step.
Thank you.

Suppose that when $n=k$ $(k≥4)$, we have that $k!>2^k$.
Now, we have to prove that $(k+1)!>2^{k+1}$ when $n=(k+1) (k≥4)$.
$(k+1)! = (k+1)k! > (k+1)2^k$    (since $k!>2^k$)
That implies 
      $(k+1)!>2^k \cdot 2$      (since $(k+1)>2$ because of $k$ is greater than or equal to $4$)
Therefore, $(k+1)!>2^{k+1}$
Finally,  we may conclude that $n!>2^n$ for all integers $n≥4$
