1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    lanedance

    User Avatar
    Homework Helper

    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

    lanedance

    User Avatar
    Homework Helper

    welcome to PF by the way
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook