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    Radius of Convergence of the Power Series

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    Complex Variable
    Radius of Convergence of the Power Series

    ∞ ∞
    Theorem:- ∑ anzn is a power series and ∑ nanzn - 1 is the power series obtained
    n=0 n=0
    by differentiating the first series term by term.
    Then the derived series has the same radius of convergence as the original series.

    See the attached file.

    © BrainMass Inc. brainmass.com October 9, 2019, 4:37 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/radius-of-convergence-of-the-power-series-37244

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    Complex Variable
    Radius of Convergence of the Power Series
    ...

    Solution Summary

    This solution is comprised of a detailed explanation of the radius of convergence of the
    ∞
    power series ∑ anzn.
    n=0
    It contains step-by-step explanation for the following problem:
    ∞ ∞
    Theorem:- ∑ anzn is a power series and ∑ nanzn - 1 is the power series obtained
    n=0 n=0
    by differentiating the first series term by term.

    Then the derived series has the same radius of convergence as the original series.

    Solution contains detailed step-by-step explanation.

    $2.19