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Math Help - alternating series

  1. #1
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    alternating series

    sum_(n=-1)^infinity(-1)^(n+1) (1/3)^n = 9/4~~2.25...

    How do you prove that? Is there a certain formula to figure out the sum of the alternating series?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Brotha View Post
    sum_(n=-1)^infinity(-1)^(n+1) (1/3)^n = 9/4~~2.25...

    How do you prove that? Is there a certain formula to figure out the sum of the alternating series?
    It appears to be geometric in form. Observe that:

    \sum_{n=-1}^{\infty}(-1)^{n+1}\left(\tfrac{1}{3}\right)^n=3-\sum_{n=0}^{\infty}\left(-\tfrac{1}{3}\right)^n=\ldots

    Can you finish this?
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