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Math Help - Principle of Mathy Induction.........

  1. #1
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    Principle of Mathy Induction.........

    State the principle of mathematical induction and use it to prove that;

    1^2+2^2+3^2+...+n^2=1/6n(n+1)(2n+1)
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  2. #2
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    Presume P_{1} is true, since \frac{(1)(1+1)(2(1)+1)}{6}=1

    Presume P_{k} is true:

    1^{2}+2^{2}+3^{2}+...........+k^{2}=\frac{k(k+1)(2  k+1)}{6}

    Therefore,

    1^{2}+2^{2}+3^{2}+............+k^{2}+(k+1)^{2}= \frac{k(k+1)(2k+1)}{6}+(k+1)^{2}

    = (k+1)\left[\frac{k(2k+1)}{6}+\frac{6(k+1)}{6}\right]

    = \frac{(k+1)(2k^{2}+7k+6}{6})

    = \frac{(k+1)(k+2)(2k+3)}{6}

    So, P_{k+1} is true. QED
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