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Math Help - inversion of formal series

  1. #1
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    inversion of formal series

    Hello!

    I have a formal power series: f(x) = 1 + x + x^2 + x^3 + ... and I have to find a series g(x): g(x) = {1 \over f(x)}.

    Using the formula found on Wikipedia Formal power series - Wikipedia, the free encyclopedia I've got this result: g(x) = 1 - x. I see this result as very strange. How can I check it?
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  2. #2
    MHF Contributor chisigma's Avatar
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    For |x|<1 is...

    \displaystyle f(x)=\frac{1}{1-x} = 1+x+x^{2}+x^{3} + ... (1)

    ... so that is [simply]...

    \displaystyle \frac{1}{f(x)} = 1-x (2)

    Kind regards

    \chi \sigma
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