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Math Help - Coefficient of nth term in binomial series

  1. #1
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    Coefficient of nth term in binomial series

    Hi Guys,

    Another binomial expansion problem.

    Write down the first 4 terms and the coefficient of x^n in the expansions in ascending powers of x of the following expression.

    (1 - 2x)^{\frac{1}{2}}

    I got the first part, by expanding it as a binomial series,

    1 - x - \frac{1}{2}x^2 - \frac{1}{2}x^3 + ...

    How do I find the coefficient of x^n? What kind of series are the coefficients in?

    Thanks again for all your help!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    In general, for all p\in\mathbb{R} :

    (1+x)^p=\displaystyle\sum_{n=0}^{+\infty}\binom{p}  {n}x^n \quad (|x|<1)
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  3. #3
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    Quote Originally Posted by FernandoRevilla View Post
    In general, for all p\in\mathbb{R} :

    (1+x)^p=\displaystyle\sum_{n=0}^{+\infty}\binom{p}  {n}x^n \quad (|x|<1)
    Thanks @FernandoRevilla. But how do I simplify this? 1/2! As far as I know factorials are for non-negative integers only?
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