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Math Help - binominal coefficients

  1. #1
    baz
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    binominal coefficients

    need help on this one.
    used newton's binominal and its derivative but couldnot get the result.
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by baz View Post
    need help on this one.
    used newton's binominal and its derivative but couldnot get the result.
    (1+x)^n = \displaystyle \sum_{k=0}^{k=n} \binom{n}{k}x^k

    differentiate the equation on both the sides:

    n(1+x)^{n-1} = \displaystyle \sum_{k=0}^{k=n} k\binom{n}{k}x^{k-1}

    Multiply by x on both sides:

    nx(1+x)^{n-1} = \displaystyle \sum_{k=0}^{k=n}  k\binom{n}{k}x^{k}

    Now substitute x = -1 to get your answer
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