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Math Help - Interval of Convergence for a Power Serires

  1. #1
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    Interval of Convergence for a Power Serires

    I need confirmation that I'm applying the ratio test correctly.

    \Sigma_{n=0}^{\infty}\left(\frac{n!(x-c)^n}{1\cdot 3\cdot 5\cdot\cdot\cdot (2n-1)}\right)

    \lim_{n->\infty}\mid\frac{(n+1)!(x-c)^{n+1}}{1\cdot 3\cdot 5\cdot\cdot\cdot (2n-1)(2n+3)}\frac{1\cdot 3\cdot 5\cdot\cdot\cdot (2n-1)}{n!(x-c)^n}\mid

    I'm not certain if I'm setting that up correctly.

    If it's correct, It should be easy from this point on.
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  2. #2
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    I think your (2n+3) should be (2n+1), shouldn't it? There are n terms in the multiplication of odd numbers in the denominator of the nth element of the series. Otherwise, it looks fine to me.
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  3. #3
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    Yes, that's right. I checked it.
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