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    Interval of convergence

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    Find the interval of convergence of (a) f(x), (b) f'(x), (c) f''(x), (d) {f(x)dx

    En=1 [(-1)^n+1 (x-2)^n ] / 2

    © BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/interval-convergence-functions-7741

    Solution Preview

    Solution. I guess your question is to find the interval of the series with power function term. Is the general term as follows?

    Fn(x)=1/2*[(-1)^(n+1)*(x-2)^n]
    I answer your question if Fn(x) is of the form above.

    The series F1(x)+F2(x)+...+Fn(x)+...
    =1/2*(x-2)-1/2*(x-2)^2+...+1/2*(-1)^(n+1)*(x-2)^n+...

    ...

    Solution Summary

    An interval of convergence is found.

    $2.49

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