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    Radius of Convergence : Summations and Power Series

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    a) Evaluate

    b) What is the radus of convergence ....
    To what simple function does this series converge?
    c) Is f(z)=...
    analytic near z= -1? and expand f(z)=
    in a power series near z= -1 can we predict the domain of convergence from the outset?

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    Solution Preview

    See attachment please!

    a. Evaluate and

    Solution. (1) By a formula for n-th derivative

    we know that

    if ; otherwise, since is analytic at .
    . ...

    Solution Summary

    Convergenc of series is investigated. The solution is detailed and well-presented.