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Math Help - Finding the Sum of an Infinite Series

  1. #1
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    Finding the Sum of an Infinite Series

    http://www-users.math.umd.edu/~wojte...d_3_sample.pdf

    It's #2.

    Note: This is only a sample exam.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    We have:

    \displaystyle\sum_{k=1}^{\infty}\dfrac{(-1)^k4^{k-1}}{3^{2k}}}=\dfrac{1}{4}\displaystyle\sum_{k=1}^{  \infty}\left(\frac{-4}{9}\right)^k=\ldots

    Now, use a well known theorem about geometric series.

    Regards.

    Fernando Revilla
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  3. #3
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    @Fernando: Thanks! I'm not the best at manipulating series :P
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by kgarcia3 View Post
    @Fernando: Thanks! I'm not the best at manipulating series :P
    Neither do I.

    Regards.

    Fernando Revilla
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