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Math Help - Biniomial Theorem Question / Combinations questions

  1. #1
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    Biniomial Theorem Question / Combinations questions

    (30C1)/2 + (30C3)/4 + (30C5)/6 ...... (30C29)/30

    any help in this would be helpful. Completely lost.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \frac{C_{30}^{2k-1}}{2k}=\frac{1}{2k}\cdot\frac{30!}{(2k)!(30-2k+1)!}=\frac{30!}{(2k)!(31-2k)!}=

    =\frac{1}{31}\cdot\frac{31!}{(2k)!(31-2k)!}=\frac{1}{31}C_{31}^{2k}

    \frac{C_{30}^1}{2}+\frac{C_{30}^3}{4}+\ldots+\frac  {C_{30}^{29}}{30}=\frac{1}{31}(C_{31}^2+C_{31}^4+\  ldots+C_{31}^{30})=

    =\frac{1}{31}(2^{30}-1)
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  3. #3
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    GOT it! thanks
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