I'm trying to prove that $n! &gt; n^2$ for $n\geq 4$ by use of mathematical induction, but I get to the inductive step and get lost. But I'm struggling with the inductive step as expected.
How can I show that $n^2&lt;n!$ for all $n\geq 4$ Step 1 For $n=1$, the LHS=$4^2=16$ and RHS=$4!=24$. So LHS$&lt;$ RHS. Step 2 Suppose the result be true for $n=k$  i.e., $k^2&lt;k!$ Step 3 For $n=k+1$ $(k+1)^2=k^2+2k+1$ What will be the next step?
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