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Thread: Binomial coefficients

  1. February 24th 2009, 10:52 PM #1
    pankaj
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    Binomial coefficients

    Evaluate
    <br /> \sum_{r = 1}^{n}( - 1)^r(1 + \frac {1}{2} + \frac {1}{3} + ...... + \frac {1}{r})\binom{n}{r}<br />
    where \binom{n}{r} is the binomial coefficient
    Last edited by pankaj; February 25th 2009 at 05:19 PM.
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  2. February 25th 2009, 05:18 PM #2
    pankaj
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    Replace \binom{n}{r} by \binom{n-1}{r-1}+\binom{n-1}{r} and see how the series simplifies
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