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    Real Analysis : Radius and Interval of Convergence - Power Series (3 Problems)

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    Determine the radius of convergence and the exact interval of convergence of the following power series...

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    https://brainmass.com/math/real-analysis/real-analysis-radius-interval-convergence-power-series-31014

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    Solution.

    (a) For
    We know that if a power series converges, then it converges absolutely. So, we consider . We have the ratio of the n+1 term and the n-th term is

    If , then converges. So,
    converges. So, we know that the radius of the convergence is .

    Now we consider ...

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