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Math Help - Series test

  1. #1
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    Series test

    Which test do I use for this series to see if it converges?

    \sum_{n=1}^{\infty}\frac{n!}{1*3*5...(2n-1)}

    Thanks
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  2. #2
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    Quote Originally Posted by JJ007 View Post
    Which test do I use for this series to see if it converges?

    \sum_{n=1}^{\infty}\frac{n!}{1*3*5...(2n-1)}

    Thanks

    \frac{n!}{1\cdot 3\cdot 5\cdot\ldots\cdot (2n-1)}=\frac{n!(2\cdot 4\cdot 6\cdot \ldots \cdot 2n)}{1\cdot 2\cdot 3\cdot 4\cdot \ldots\cdot (2n-1)(2n)}=\frac{2^n(n!)^2}{(2n)!}

    Now you can use D'Alembert's test (= quotient test) to check it does converge.

    Tonio
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