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Math Help - proof by induction

  1. #1
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    proof by induction

    prove by mathematical induction, that for n

     \sum_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1)

    assume that the summation formula is true for n=k

     \sum_{i=1}^n i^{2} = \frac{1}{6} k (k+1) (2k+1)

    so must be true for n= k+1 ?

    so do I put k+1 into the formula, and try and get it match the original? really stuck from this part,


    Last edited by Tweety; May 23rd 2012 at 08:00 AM.
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  2. #2
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    Re: proof by induction

    Quote Originally Posted by Tweety View Post
    prove by mathematical induction, that for n

     \sum_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1)

    assume that the summation formula is true for n=k

     \sum_{i=1}^n i^{2} = \frac{1}{6} k (k+1) (2k+1)

    so must be true for n= k+1 ?

    so do I put k+1 into the formula, and try and get it match the original? really stuck from this part,
    Note  \sum_{i=1}^{n+1} i^{2} =\sum_{i=1}^n i^{2} +(n+1)^2
    Thanks from Tweety
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