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Math Help - Power Series Problem - # 2

  1. #1
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    Power Series Problem - # 2

    Find the power series representation for the function, and the interval of convergence.

    f(x) = \dfrac{1}{1 + x} = \dfrac{1}{1 - (-x)} = Summation sign goes here - n = 0 to infinity (-x)^{n} ??? Why is there an "n" power here over (-x) ??

    Summation sign goes here - n = 0 to infinity (-1)^{n} x^{n} ??? What is going on here?

    |-x| < 1

    |x| < 1

    R = 1 ??

    I = (-1,1)
    Last edited by Jason76; August 1st 2014 at 08:35 PM.
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  2. #2
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    Re: Power Series Problem - # 2

    It's always based on 1/(1-x) = sum (n=0 ~ inf.) x^n. Now we are just replacing x with -x.
    If you don't think it's making sense, it's because this only works if |x| < 1.
    By the way, I tried with x=0.6, and playing with the first 10 terms did give me something near 0.625. xD
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