Explore BrainMass

Explore BrainMass

    Radius of Convergence : Summations and Power Series

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file for full problem description.

    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?

    © BrainMass Inc. brainmass.com December 24, 2021, 5:03 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/radius-convergence-summations-power-series-24436

    Attachments

    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.

    $2.49

    ADVERTISEMENT