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Math Help - Prove by induction

  1. #1
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    Prove by induction

    Prove by induction:1*2+2*3+3*4+...+n(n+1)=n(n+1)(n+2)/3
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  2. #2
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    Quote Originally Posted by sderosa518 View Post
    Prove by induction:1*2+2*3+3*4+...+n(n+1)=n(n+1)(n+2)/3
    Base case: n=1

    1 \cdot 2 = \frac{1 \cdot 2 \cdot 3}{3} = 1 \cdot 2

    Assume correctness for n=k. Prove for n=k+1:

    LHS:
    1 \cdot 2 + 2 \cdot 3 + ... + n(n+1) + (n+1)(n+2) = \frac{n(n+1)(n+2)}{3} + (n+1)(n+2) =  \frac{n(n+1)(n+2)}{3} + \frac{3(n+1)(n+2)}{3} = \frac{n(n+1)(n+2) + 3(n+1)(n+2)}{3} = \frac{(n+1)(n+2)(n+3)}{3}

    RHS:
    \frac{(n+1)(n+2)(n+3)}{3}
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