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Math Help - Find power series representation and interval of convergence.

  1. #1
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    Find power series representation and interval of convergence.

    The problem:

    \[f(x) = 1 / (1+9x^2)\]

    My attempt:

    f(x) = 1 / (1-(-9x^2)) = \sum (-9x^2)^n = \sum (-1)^n(9x^2)^n

    With |-9x^2| < 1, 9x < 1, x < 1/9
    R = 1/9, I = (-1/9, 1/9)

    Not sure if this is correct. Thanks
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  2. #2
    MHF Contributor

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    Re: Find power series representation and interval of convergence.

    That's a good way to start: you recognized that \frac{1}{1- r} is the sum of the geometric series \sum r^n and here r= -9x^2[/tex]. However, 9x^2< 1 does NOT give 9x< 1, it gives 9x^2< 1 so that -\frac{1}{3}< x< \frac{1}{3}
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  3. #3
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    Re: Find power series representation and interval of convergence.

    You're right, rookie mistake
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