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Math Help - need induction proof help

  1. #1
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    need induction proof help

    \sum_{k=0}^nk^3=\left(\sum_{k=0}^nk \right)^2
    i did use the base case and find it true
    1=1
    0^3+1^3=0+1*0+1
    im not good with latex but in my paper the right side just to make it more "simple" for me i did write it as 2 times that instend to have ^2...
    ima proof for k+1 and need tips :S im lost
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  2. #2
    fkf
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    Re: need induction proof help

    You can use the fact that the right side is just a square of a ordinary arithmetic sum.
    sum = n/2(a_1+a_n)
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  3. #3
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    Re: need induction proof help

    Quote Originally Posted by Petrus View Post
    \sum_{k=1}^nk^3=\left(\sum_{k=1}^nk \right)^2
    If I were you, I would note that \left(\sum_{k=1}^nk \right)^2=\frac{n^2(n+1)^2}{4}

    Then the inductive step becomes
    \sum_{k=1}^{n+1}k^3=\sum_{k=1}^nk^3+(n+1)^3=\frac{  n^2(n+1)^2}{4}+(n+1)^3
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: need induction proof help

    This is an exercise I gave to the OP to practice induction, and the suggestion given by Plato is exactly what I had in mind.
    Thanks from Petrus
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