Use induction to prove that $n! > 3n$ for $n\ge4 $.
I have done the base case and got both sides being equal to $24>12$ for $n=4$. However, when doing the inductive step I can't seem to find the right form to match the expression on the right hand side.
So far I have:
Need to show: $(n+1)!>3(n+1)$.
When doing the inductive step:
$(n+1)! = (n+1)n!$
we know that $n!$ is larger than $3n$, then
Here is where I don't know what to do next, could anyone shed some insight on how to continue after this part? Thanks.