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Math Help - Power Series

  1. #1
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    Power Series

    From the power series,

    x - \frac{x^2}{2} + \frac{x^3}{3} - ... + (-1)^{n-1} \frac{x^n}{n} + ... = \ln (1 + x),

    obtain the power series whose sum is

    \ln (\frac{1+x}{1-x}).
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  2. #2
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    Quote Originally Posted by cgiulz View Post
    From the power series,

    x - \frac{x^2}{2} + \frac{x^3}{3} - ... + (-1)^{n-1} \frac{x^n}{n} + ... = \ln (1 + x),

    obtain the power series whose sum is

    \ln (\frac{1+x}{1-x}).

    (1+x)/(1-x) = 1 + 2x/(1-x) ==> simmilarly as the above one we get:

    ln(1 - 2x/(1-x)) = 2x/(1-x) - [2x/(1-x)]^2/2 + [2x/(1-x)]^3/3 -....

    Tonio
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  3. #3
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    \ln (1+x)-\ln (1-x)=\ln (1+x)-\ln \big(1+(-x)\big).
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