Stuck at this induction problem I am giving it everything, but i just can't get it right. The problem: Prove by induction that $n!>2^n$ for all integers $n\ge4$ I know how to solve the basic induction problems, but no matter what I do, I can't get this one right. I saw how the problem is solved (schoolmate uploaded it on our class dropbox), but I just don't understand it. The problem is, we only worked on the basics. If someone could explain this like I'm five, that would be appreciated

For $n=4$, we have that $4!=24>16=2^4$, so the condition holds. Now assume it's valid for $k\geq4$: $k!>2^k$. Then $$(k+1)!=(k+1)k!>(k+1)2^k>2\cdot2^k=2^{k+1},$$ and we hake that the condition holds for $k+1$.