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Comparison Tests for Series

  1. Jul 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Does the following series converge or diverge (use either the Limit Comparison or the Direct Comparison Test):

    [tex]\sum_{n=1}^{+\infty} \frac{3^{n-1}+1}{3^{n}}[/tex]


    2. Relevant equations

    In a previous problem that was
    [tex]\sum_{n=1}^{+\infty} \frac{1}{3^{n-1}+1}[/tex]
    I was able to reindex the series to make it
    [tex]\sum_{n=0}^{+\infty} \frac{1}{3^{n}+1}[/tex]
    From there, I took 1/(3n+1)<1/3n.

    Therefore, since 1/3n converges, [tex]\sum_{n=1}^{+\infty} a_{n}[/tex] also converges.


    3. The attempt at a solution

    However, I don't know how to solve the series that I'm currently on.

    Thanks,
    Erik
     
  2. jcsd
  3. Jul 6, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    (3^(n-1)+1)/3^n>1/3, isn't it?
     
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