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Convergence of a series

  1. Nov 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the radius of convergence and the interval of convergence for
    \sum_{n=0}^\infty \frac{x^n}{n3^n}


    2. Relevant equations

    3. The attempt at a solution
    Ok, so I first applied the ratio test.

    \frac{x^{n+1}}{(n+1)3^(n+1)} /

    After some cancellations I got

    L = |x/3|


    Does this mean that the interval of convergence is from -3<x<3 ?
  2. jcsd
  3. Nov 3, 2009 #2


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  4. Nov 4, 2009 #3


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    You have to check the endpoints of your interval separately to see if the series converges there since the ratio test doesn't give any information when the limit is 1
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