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    Functions : Radius of Convergence and Approximations

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    Let f be the function defined by f(x) = sigma (starting at n=1 ending at infinity)

    xnnn /(3n n!) for all values of x for which the series converges.

    a) Find the radius of convergence of this series
    b) Use the first three terms of this series to approximate f(-1)
    c) Estimate the amount of error involved in the approximation in part b. Justify your answer

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    https://brainmass.com/math/graphs-and-functions/functions-radius-convergence-approximations-17185

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    a)
    an=x^n*n^n /(3^n*n!)
    an+1=x^(n+1)*(n+1)^(n+1) /(3^(n+1)*(n+1)!)

    |an+1/an|=|1/3*x*(n+1)^n/(n^n)|

    lim|1/3*x*(n+1)^n/(n^n)|=|ex/3|
    n--->infinity

    Note ...

    Solution Summary

    The radius of convergence and an approximation of a function are found.

    $2.19

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