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 $n\ge 3$


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*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.

HINT: $(k+2)^2=\big((k+1)+1\big)^2=(k+1)^2+2(k+1)+1$; now apply the induction hypothesis that $(k+1)^2<2k^2$. (There will still be a bit of work to do; in particular, you’ll have to use the fact that $k\ge 1$.)
