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Math Help - Binomial Theorem with fractional exponents

  1. #1
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    Binomial Theorem with fractional exponents

    What's the 3rd term of (8x-y)^(1/3)?

    Can you use the binomial theorem for this? Because I dont know how you can find out the coefficient. Because you cant find out ((1/3) choose 2). So how would you find the answer?
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  2. #2
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    actually you can, but it's not easy ... finding factorials of fractions involves the Gamma function if I remember correctly.
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  3. #3
    Moo
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    Hello,

    {r \choose n}=\frac{1}{n!} \prod_{k=0}^{n-1} (r-k)=\frac{(r-1)(r-2)\dots(r-n+1)}{n!}

    Here, n=2 and r=1/3
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