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Math Help - Proof of summation of i^3 by induction, help needed

  1. #1
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    Proof of summation of i^3 by induction, help needed


    This is my first proof using induction and, as expected, I'm stuck. In fact, I don't know where to start. Any help is appreciated. THanks.
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  2. #2
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    Quote Originally Posted by qtpipi View Post

    This is my first proof using induction and, as expected, I'm stuck. In fact, I don't know where to start. Any help is appreciated. THanks.
    Start with the base case, when n=1 is it true?

    Then the induction step is to assume it true for n=k, and show that implies that it is true when n=k+1.

    So you need to show that the assumption that:

    \sum_{i=1}^ki^3=\left(\frac{k(k+1)}{2} \right)^2

    implies that:

    \sum_{i=1}^{k+1}i^3 = \left(\sum_{i=1}^ki^3\right) + (k+1)^3=\left(\frac{(k+1)(k+2)}{2} \right)^2

    CB
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