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Calculus question involving an infinite series

  1. Apr 4, 2010 #1
    The series from n = 1 infinity of 1/(n*(3^n)) must

    A) converge to a value greater than 1/4
    B) converge to a value greater than 1/9
    C) Converge to a value less than 1/8
    D) converge to a value less than 1/2
    E) diverge.

    I know the series definitely does not diverge because the series (1/3)^n is a geometric series which converges and the series is question is smaller than that geometric series so it much converge by the direct comparision test.

    But I am not sure how to see what it would converge to. Can someone help?
  2. jcsd
  3. Apr 5, 2010 #2
    Given the multiple choices, just look at the first term in your infinite series. What can you conclude?
  4. Apr 5, 2010 #3


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    so you've ruled out E)

    couple of things to consider...
    - what does 1/3^n converge to? then what can you say about each term of your series relative to that series

    - what do the first few terms add upto, can you rule out any other answers?
  5. Apr 5, 2010 #4


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    welcome to PF by the way
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