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Help with simple proof by mathematical induction

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    0^2 + 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6

    2. Relevant equations

    3. The attempt at a solution

    I'm confused on how to prove this by induction. I'm not exactly sure what the goal of the rearrangement is after substituting (n+1). Any help is much appreciated!

    base case: n = 0
    0^2 = 0(0+1)(2*0+1)/6

    induction step:
    (0^2+1^2+2^2+...+n^2) + (n+1)^2 = (n+1)((n+1)+1)(2(n+1)+1)/6

    n(n+1)(2n+1)/6 + (n+1)^2

    (n+1)[n(2n+1)/6 + (n+1)]
    ...here is where I'm lost, I'm not sure what I'm trying to manipulate it to look like....

  2. jcsd
  3. May 2, 2010 #2


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    Homework Helper

    Factor out 1/6 and then simplify what is left in the brackets.
  4. May 2, 2010 #3


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    Staff Emeritus
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    You're trying to show the first equation is true. To do this, you start with one side, as you have done, and manipulate it until it looks like the other side.
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