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Series help

  1. Sep 4, 2007 #1

    fsm

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    1. The problem statement, all variables and given/known data
    [tex]\sum (1+2^n)/3^n[/tex]

    Find its sum


    2. Relevant equations



    3. The attempt at a solution
    I don't know how to figure this one out. I took the limit and it was zero so I know it converges. I dont know where to start on this one. The answer is 5/2.
     
  2. jcsd
  3. Sep 4, 2007 #2
    Write this as the sum of two summations.
     
  4. Sep 5, 2007 #3

    HallsofIvy

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    More precisely, the sum of two geometric series.
     
  5. Sep 6, 2007 #4

    Gib Z

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    And just because the the terms approach zero, the series always convergent. Think of the harmonic series.
     
  6. Sep 6, 2007 #5

    HallsofIvy

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    Typo? I'm quite sure Gib Z meant "just because the terms approach zero, the series is not always convergent". Yes, this particular series converges but your statement " I took the limit (of the sequence of terms) and it was zero so I know it converges" does not follow.
    The fact that the limit of the sequence of terms goes to zero is necessary for convergence but not sufficient.
     
  7. Sep 6, 2007 #6

    Gib Z

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    Typo indeed :( Was in a rush for that post lol.
     
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