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Math Help - Power series to approximate definite integral

  1. #1
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    Power series to approximate definite integral

    So i need to approximate the integral from 0 to 0.2 of x/(1-x)
    with error less than 1/1000.

    so i let f(x) = x/(1-x)

    = summation n=0 to infinity ( x^(n+1))

    so i take the integral of the summation to get:

    summation n=0 to infinity ( x^(n+2)/(n+2) )

    If the series was alternating I would know how to calculate it with error to 1/1000 but I don't know how to do this if it isn't alternating.
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  2. #2
    MHF Contributor matheagle's Avatar
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    There are various forms for the remainder term, such as LaGrange
    Taylor's theorem - Wikipedia, the free encyclopedia

    And you can check your work easily since

    {x\over 1-x}=-1+{1\over 1-x}

    and I get -.2-\ln (.8)\approx .023143551 as the answer/limit.
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