Proving the following inequality using Mathematical Induction I need to prove the following inequality is true for n > 2.
$n^3$ > 2$n^2$ + 3


*

*Prove using base case n = 3:


$3^3$ > 2$(3)^2$ + 3
27 > 2(9) + 3
27 > 18 + 3
27 > 21 (true)


*Assume true for n = k:


$k^3$ > 2$k^2$ + 3


*Prove for n = k +1


$(k+1)^3$ > 2$(k+1)^2$ + 3
I'm not sure where to go from here. I'm thinking I may need to prove it for n = k +2 (since I'm proving the expression is true for n > 2), but I'm not sure. How would I be able to prove this using n = k + 1?

Now, $$(k+1)^3=k^3+3k^2+3k+1=2(k+1)^2+3+k^3+k^2-k-4>2(k+1)^2+3.$$
