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Math Help - Power Series problem

  1. #1
    spd579
    Guest

    Power Series problem

    ((-1)^n(x^n))/(11^n(n^2+5))

    i seem to come up with the problem being convergent from -1/11 to 1/11 but it's telling me thats not right. any ideas? thanks , Drew
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  2. #2
    Super Member

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    Hello, spd579!

    A simple error . . . somewhere.


    \frac{(-1)^nx^n}{11^n(n^2+5)}

    Ratio Test

    . . \left|\frac{a_{n+1}}{a_n}\right| \;=\;\left|\frac{x^{n+1}}{11^{n+1}[(n+1)^2+5]}\cdot\frac{11^n(n^2+5)}{x^n}\right| = \;\left|\frac{x}{11}\cdot\frac{n^2+5}{n^2 + 2n + 6}\right|


    Divide top and bottom by n^2 and take the limit.

    . . R \;= \;\lim_{n\to\infty}\left|\frac{x}{11}\cdot\frac{1 + \frac{5}{n^2}}{1 + \frac{2}{n} + \frac{6}{n^2}}\right| \;=\;\left|\frac{x}{11}\right|

    Since \left|\frac{x}{11}\right| < 1, we have: .  -11 < x < 11


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