using induction to prove $(n+1)^2 < 2n^2$ (Im not English and just started doing maths in English so my termiology is still way off)
So the title for $n\ge 3$


*

*First I use calculate both sides with $3$, which is true 

*I make my induction. $(k+1)^2 < 2k^2$
then I replace $N$ with $k+1$:   $(k+2)^2 < 2(k+1)^2$
Now what? I cant seem to find how to use my induction in this one. I've also tried working out the brackets, but that also didn't seem to help me.

1.Basis
First we check for the smallest number: $n=3$
$$4^2 < 2*3^2$$
$$16 < 18$$
2.Inductive Hypothesis
$$(k+1)^2 < 2k^2$$
3.Inductive step
$$(k+2)^2 < 2(k+1)^2$$
$$k^2 + 4k + 4 < 2k^2 + 4k + 2$$
$$4 < k^2 + 2$$
Which is true for every $n \geq 3$
