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Math Help - Induction

  1. #1
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    Induction

    Prove: for all n is an element N

    N = natural numbers

    n
    Sigma Notation (3k^2 - 3k + 1) = n^3
    k=1
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  2. #2
    Senior Member vincisonfire's Avatar
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    *\sum_{k=1}^{n} 3k^2-3k+1 = n^3

     \sum_{k=1}^{n+1} 3k^2-3k+1 = \sum_{k=1}^{n} 3k^2-3k+1 + 3(n+1)^2-3(n+1)+ 1

    = n^3  + 3(n+1)^2-3(n+1)+ 1 = n^3 + 3n^2 + 3n +1 = (n+1)^3
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