# Math Induction problem

## Homework Statement

We are asked to try and prove the values n where n2 < 2(n) .
It asks us to prove it by Math Induction.

## The Attempt at a Solution

I can see it works for n=0 and n=1 but not for n=2,3,4 . So I made my base step n=5 and showed that 52 = 25 < 25 =32 as 25<32. I then started simple mathematical induction off by assuming that n2<2n for n>5, and tried to prove it using (n+1)2<2(n+1) but can't seem to get that proven. Any suggested help on how to prove that?

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It seems that you need to show that $$2n+1<2^n$$... Maybe another induction?

yes that is exactly what I had to do, I assume it is sufficient to have an induction proof within an induction proof?

I cant really see a problem with that...