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Finding the sum of a Series that is converge or Diverge

  1. Mar 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Determine whether the series is either Converge or Diverge, if it's convergent, find its sum

    ∑ from n=1 to ∞ of (1+2^n)/(3^n)

    2. Relevant equations

    3. The attempt at a solution

    1) i replaced the (1+2^n) to just (2^n) and my equation behaves like ∑ (2/3)^n which the Radius (2/3) < 1. So it's Convergent.
    2) I found that my leading term was 2/3 by n=1
    3) i plug everything in to my Geometric series formula (2/3)/(1-(2/3), thus giving me an answer of 2.

    Problem: the Books answer was 5/2. Can anyone help me out? Thanks!
  2. jcsd
  3. Mar 20, 2014 #2


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    Homework Helper

    You can't throw away the 1 if you expect to get an exact sum. Put it back in.
  4. Mar 20, 2014 #3
    Yes, keep the 1 inside. I understand your idea for breaking up the sum, but you forgot about the other term.

    Your split idea is good: (1+2^n)/(3^n) = 1/3^n + 2^n/3^n.

    Use your formula for both these terms. Hint: 1 = 1^n.
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