SOLUTION: Prove by induction that 2^n>=n^2. I was stocked at the induction step when 2^(k+1)>=2k^2

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Question 527962: Prove by induction that 2^n>=n^2. I was stocked at the induction step when 2^(k+1)>=2k^2
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The induction basically claims that if for some k > 1, if

, then

.

Since , we can construct the inequality



The inequality is equivalent to It factors to , which is true for sufficiently large k (it doesn't hold for k = 0,1,2 but we can check these cases separately).