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Math Help - Sum of convergent series

  1. #1
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    Sum of convergent series

    Ok, so here is my problem:

    Find the sum of the convergent series:

    \sum_{n=0}^{\infty }\frac{(-1)^n\pi ^{2n+1}}{3^{2n+1}(2n+1)!}

    Im wondering if someone can push me in the right direction of this.. Do I find partials sums and then find an nth term from those partial sums? Help on this would be much appreciated!
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  2. #2
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    Quote Originally Posted by intervade View Post
    Ok, so here is my problem:

    Find the sum of the convergent series:

    \sum_{n=0}^{\infty }\frac{(-1)^n\pi ^{2n+1}}{3^{2n+1}(2n+1)!}

    Im wondering if someone can push me in the right direction of this.. Do I find partials sums and then find an nth term from those partial sums? Help on this would be much appreciated!
    hint ... what function does this series represent ?

    \sum_{n=0}^{\infty }\frac{(-1)^n x^{2n+1}}{(2n+1)!}
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  3. #3
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    Well, that function represents the sin(x) but I'm really not sure where the 3^(2n+1) comes in at all.
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  4. #4
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    Quote Originally Posted by intervade View Post
    Well, that function represents the sin(x) but I'm really not sure where the 3^(2n+1) comes in at all.
    x^{2n+1} = \left(\frac{\pi}{3}\right)^{2n+1}
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