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Math Help - Power Project

  1. #1
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    Power Project

    Some help with this question would be greatly appreciated!

    Determine for which natural numbers k^2 < 2^k and prove your answer.

    Power is defined in the following way. Let b be a fixed integer. We define b^k for all integers k >= 0 by:

    b^0 := 1

    Assuming b^n defined, let b^(n+1) := b^n * b

    Thanks!
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  2. #2
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    Quote Originally Posted by jstarks44444 View Post
    Some help with this question would be greatly appreciated!
    Determine for which natural numbers k^2 < 2^k and prove your answer.
    Is it true for k=1,~2,~3\text{ or }4~?
    By induction show that if n\ge5 then n^2<2^n.
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