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Math Help - Mathematical Induction Proof

  1. #1
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    Mathematical Induction Proof

    My question is to prove this by Induction, 1^3 + 2^3 + + n^3 = n^2(n+1)^2/4

    I got the base step, but I am struggling on the Inductive Step. Here is what I have:
    Assume Pk is true
    Consider Pk+1
    Σ i^3 (from i=1 to k+1) = Σ i^3 (from i=1 to k) + (k+1)
    = k^2(k+1)/4 + (k+1)
    = (k+1)[k(k+1)/4 + 1]
    = (k+1)[k(k+1)+4/4]
    Therefore, by Induction Pn is true for all n≥1
    I was told that my answer is incorrect. Any help on where I went wrong?
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  2. #2
    MHF Contributor
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    Thanks
    1
    Quote Originally Posted by page929 View Post
    My question is to prove this by Induction, 1^3 + 2^3 + + n^3 = n^2(n+1)^2/4

    I got the base step, but I am struggling on the Inductive Step. Here is what I have:
    Assume Pk is true
    Consider Pk+1
    Σ i^3 (from i=1 to k+1) = Σ i^3 (from i=1 to k) + (k+1) incorrect
    = k^2(k+1)/4 + (k+1)
    = (k+1)[k(k+1)/4 + 1]
    = (k+1)[k(k+1)+4/4]
    Therefore, by Induction Pn is true for all n≥1
    I was told that my answer is incorrect. Any help on where I went wrong?
    Hi page929,

    As you are summing cubes,

    \displaystyle\sum_{i=1}^{ k+1}i^3=1^3+2^3+...+k^3+(k+1)^3=\sum_{i=1}^ki^3+(k  +1)^3

    and you should be attempting to show that this is \displaystyle\frac{(k+1)^2(k+1+1)^2}{4}
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  3. #3
    Junior Member
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    I think I have it now. Thanks,
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