Proof by Induction: $n! > 2^{n+1}$ for all integers $n \geq 5.$ I have to answer this question for my math class and am having a little trouble with it. 
Use mathematical induction to prove that $n! > 2^{n+1}$ for all integers $n \geq 5.$ 
For the basis step: $(n = 5)$
$5! = 120$
$2^{5+1} = 2^6 = 64$
So $120 > 64$, which is true.
For the induction step, this is as far as I've gotten: 
Prove that $(n! > 2^{n+1}) \rightarrow \left((n+1)! > 2^{(n+1)+1}\right)$
Assume $n! > 2^{(n+1)}$
Then $(n+1)! = (n+1) \cdot n!$
After this, I'm stuck. Any assistance would be appreciated. 
Thanks! 

$(n+1)!=(n+1)\times n!>(n+1)2^{n+1}>2\times2^{n+1}=2^{n+2}$
Make sure you understand all the steps and ask if you got trouble.
