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Math Help - Induction

  1. #1
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    Induction

    P(n)=1*2*3+2*3*4+..+n(n+1)(n+2)={n(n+1)(n+2)(n+3)}/{4}

    Assume P(n), then P(n+1)= 1*2*3+2*3*4+..+n(n+1)(n+2)+(n+1)(n+2)(n+3)= {(n+1)(n+2)(n+3)(n+4)}/{4}

    So, P(n+1) = 1*2*3+2*3*4+..+n(n+1)(n+2)+(n+1)(n+2)(n+3)
    = {n(n+1)(n+2)(n+3)}/{4}+(n+1)(n+2)(n+3)
    = (k+1)(k+2)(k+3)({k}/{4}+1)

    Now I can't figure out how to get my answer to equal {(n+1)(n+2)(n+3)(n+4)}/{4}
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  2. #2
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    P(n+1) = P(n) + (n+1)(n+2)(n+3)

    P(n+1) = \frac{n(n+1)(n+2)(n+3)}{4} + \frac{4(n+1)(n+2)(n+3)}{4}

    P(n+1) = \frac{n(n+1)(n+2)(n+3) + 4(n+1)(n+2)(n+3)}{4}

    P(n+1) = \frac{(n+1)(n+2)(n+3)(n + 4)}{4}
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  3. #3
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    Question How did you simplify that?

    How did you get from

    to

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  4. #4
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    Quote Originally Posted by jennifer1004 View Post
    How did you get from

    to

    Factor like terms.
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  5. #5
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    Talking Thanks

    Duh! I feel silly. Thanks a bunch!
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