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Math Help - Simple Proof by Induction

  1. #1
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    Simple Proof by Induction

    Use induction to prove that for every integer n \geq 4, 3^n > n^3 .

    Here's the solution:



    I don't understand where the term k^3+3k^2+4k came from in the middle line. Could anyone explain?
    Last edited by Roam; October 24th 2009 at 09:37 PM.
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  2. #2
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    Quote Originally Posted by Roam View Post
    Use induction to prove that for every integer n \geq 4, 3^n > n^3 .

    Here's the solution:



    I don't understand where the term k^3+3k^2+4k came from in the middle line. Could anyone explain?
    Since k \ge 4, we know that k^3 > 3k^2 and also that k^3 > 4k. Therefore, k^3+k^3+k^3 > k^3+k^3+4k > k^3+3k^2 + 4k \Rightarrow k^3 + k^3 + k^3 > k^3 + 3k^2 + 4k
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