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Math Help - Mathematical Induction

  1. #1
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    Mathematical Induction

    I am having problems solving the second step. I have proven that n=1 in the first step.

    I have to prove each given statement through mathematical induction.





    Help would be greatly appreciated Thank you
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  2. #2
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    So now use the assumption n=k to prove n=k+1

    n=k \displaystlye 1+4+9+\dots +k^2 = \frac{k(k+1)(2k+1)}{6}

    n=k+1 \displaystlye 1+4+9+\dots +k^2 +(k+1)^2

    Using n=k for n=k+1 \displaystlye 1+4+9+\dots +k^2 +(k+1)^2 =  \frac{k(k+1)(2k+1)}{6}+(k+1)^2=\dots
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  3. #3
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    However, to add to what pickslides has written,
    you need to be aware of what you should end up with when you evaluate that sum!

    You are attempting to show that

    \displaystyle\ 1+4+9+....+k^2+(k+1)^2=\frac{(k+1)(k+2)[2(k+1)+1]}{6}

    "if"

    \displaystyle\ 1+4+9+...+k^2=\frac{k(k+1)(2k+1)}{6}
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