Originally Posted by

**morbius27** Hi, I've been working on this problem for quite a while now and I just can't seem to get the algebra working for it. Any help is appreciated.

Determine the exact set of natural numbers n for which the inequality 2^n>=(n+1)^2 holds **(1)**.

I have already found that this is true for n>=6 from intuition and plugging stuff in, but I need to prove this by induction.

Base case: n=6 holds for both sides

Induction step: I need to prove that **(1)** holds for n=k+1.

I tried plugging k+1 in for the left side, yielding 2^(k+1) = 2^k*2^1>=2*(k+1)^2 (from **(1)**) But this gets me nowhere as my ultimate goal is to arrive at 2^(k+1)>=((k+1)+1)^2

Any ideas?