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Math Help - Find the radius of convergence of a series...3x

  1. #1
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    Find the radius of convergence of a series...3x

    Dear all, Let the positive series \sum_{n=1}^\infty a_n be divergent, and \lim_{n\to\infty}\frac{a_n}{A_n}=0, where A_n=\sum_{k=1}^n a_k. Prove that the radius of convergence of the power series \sum_{n=1}^\infty a_nx^n equals 1.
    Last edited by xinglongdada; March 12th 2013 at 11:46 PM.
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  2. #2
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    Re: Find the radius of convergence of a series...3x

    My thought: Since \sum_{n=1}^\infty a_n diverges, we have the radius of convergence R\leq 1. However, I could not see how to show R<1 is impossible. 3x!
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