Prove the following using the principle of mathematic induction.
n! > n^2, for all integers n >= 4.
I am especially having trouble with the inductive step. Thanks for your help.
The way you set out these problems needs work - you need to start on one side of your statement and go through a series of arguments to get to the other side. But anyway, your logic is right at least...
$\displaystyle \displaystyle \begin{align*} ( k + 1 ) ! &= (k + 1)k! \\ &> (k + 1)k^2 \\ &> (k + 1)^2 \textrm{ since } k^2 > k + 1 \end{align*}$
It's up to you to prove $\displaystyle \displaystyle \begin{align*} k^2 > k + 1 \end{align*}$ in our region