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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
    [tex]
    \sum_{n=0}^\infty \frac{x^n}{n3^n}

    [/tex]



    2. Relevant equations



    3. The attempt at a solution
    Ok, so I first applied the ratio test.
    [tex]
    \lim_{n\rightarrow\infty}

    |
    \frac{x^{n+1}}{(n+1)3^(n+1)} /
    \frac{x^n}{n3^n}
    |
    [/tex]

    After some cancellations I got

    [tex]
    L = |x/3|

    [/tex]


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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes.
     
  4. Nov 4, 2009 #3

    Office_Shredder

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    Staff Emeritus
    Science Advisor
    Gold Member

    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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