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Homework Help: Problem with series

  1. Apr 5, 2014 #1
    1. The problem statement, all variables and given/known data

    Determine whether the series is convergent or divergent. If it is convergent, find its sum.

    2. Relevant equations

    [tex] \sum_{n=1}^{\infty} \frac{1 + 2^n}{3^n} [/tex]

    3. The attempt at a solution


    I have tried to find the sum of this series using both the limit and integral tests, but I cannot get the right answer. My answer is 1/3, but the book says it is 5/2. How can I solve this?
    Last edited: Apr 5, 2014
  2. jcsd
  3. Apr 5, 2014 #2


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    Homework Helper

    ## \sum_{n=1}^{\infty} \frac{1 + 2^n}{3^n} ##
    ## = \sum_{n=1}^{\infty} \frac{1}{3^n} + \sum_{n=1}^{\infty} \frac{2^n}{3^n} ##

    Can you see the solution now?
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