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Thread: Power Series

  1. April 25th 2008, 12:06 AM #1
    larson
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    Power Series

    I need help for the following problem.

    Find the radius of convergence for the power series:

    \sum_{j=1}^{\infty} (x/2)^j
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  2. April 25th 2008, 12:11 AM #2
    Jhevon
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by larson View Post
    I need help for the following problem.

    Find the radius of convergence for the power series:

    \sum_{j=1}^{\infty} (x/2)^j
    By the root test, the series converges for all x such that \lim_{j \to \infty} |(x/2)^j|^{1/j} < 1

    don't forget to check the end points
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  3. April 25th 2008, 01:36 AM #3
    larson
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    Quote Originally Posted by Jhevon View Post
    By the root test, the series converges for all x such that \lim_{j \to \infty} |(x/2)^j|^{1/j} < 1

    don't forget to check the end points
    how do i know what my endpoints are?
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  4. April 25th 2008, 01:48 AM #4
    Moo
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    Hello,

    Find the radius of convergence R, then look at the convergence/divergence of the series if x=R and x=-R
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