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) (Show Source): You can put this solution on YOUR website!
The induction basically claims that if for some k > 1, if
, then
^2)
.
Since  \ge 2k^2)
, we can construct the inequality
^2)
The inequality ^2)
is equivalent to 
It factors to ^2 - 2 \ge 0 \Rightarrow (k-1)^2 \ge 2)
, which is true for sufficiently large k (it doesn't hold for k = 0,1,2 but we can check these cases separately).
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