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Math Help - Radius of Convergence

  1. #1
    Senior Member slevvio's Avatar
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    Radius of Convergence

    Hello I have this question, and was wondering if anybody could help with it.

    "Find the radius of convergence of the power series

     1 +az + \frac{a(a+1)}{2!}z^2 + \cdots + \frac{a(a+1)\ldots (a+n-1)}{n!}z^n + \cdots ,

    where a is a fixed real number (the answer will depend on a)."

    However isnt that power series just  \sum_{n=0}^{\infty} \frac{ (a+n-1)!}{n!(a-1)!} z^n = \sum_{n=0}^{\infty} {a+n-1 \choose{n}} z^n, which has radius of convergence 1, which doesnt depend on a? Any help with this would be appreciated .
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    What if a is zero, or a negative integer?
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