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Math Help - Mathematical Inductions of Combinations

  1. #1
    Mel
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    Mathematical Inductions of Combinations

    If n is an integer and n > or = 2, prove recursively that the sum of the combinations C(J,2) from J=2 to N, is equal to the combination C(N+1, 3).
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    MHF Contributor red_dog's Avatar
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    C_2^2+C_3^2+C_4^2+\ldots+C_n^2=

    =(\underbrace{C_3^3+C_3^2}_{C_4^3})+C_4^2+\ldots+C  _n^2=

    =(\underbrace{C_4^3+C_4^2}_{C_5^3})+\ldots+C_n^2=

    \ldots\ldots\ldots\ldots\ldots

    =C_n^3+C_n^2=C_{n+1}^3
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