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!

Lightning SERIES question

  1. Nov 4, 2007 #1
    can anyone explain why the summation from 0 to infinity of

    (-2)^(n)/3^(n+1) diverges?

    - Is it simply because the terms bounce between - and +?
  2. jcsd
  3. Nov 4, 2007 #2
    Are you sure you wrote it correct? Because the series

    [tex] \sum_{n=0}^{\infty} \frac{(-2)^n}{3^{n+1}} [/tex]

    does converge...
  4. Nov 4, 2007 #3
    I have in the answer that it diverges...could you explain how you arrived at that?
  5. Nov 4, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper

    It's (1/3)*(-2/3)^n. It's a geometric series. You can even sum it.
  6. Nov 4, 2007 #5
    I see the light! I guess the answer key was wrong. But hey,

    What if had the SEQUENCE (-2)^(n)/3^(n+1) , how could I show that it converges to 0?

    could I also "simplify" it to (1/3)*(-2/3)^n and say that since r > -1, it converges to 0?

    (by the fact that for a sequence r^n , the sequence converges for -1 < r <= 1)
  7. Nov 4, 2007 #6


    User Avatar
    Science Advisor
    Homework Helper

    If you mean |r|<1, then yes, the sequence converges to zero.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Lightning SERIES question
  1. Lightning question (Replies: 2)

  2. Series Question (Replies: 1)

  3. Series Question (Replies: 2)

  4. A series question (Replies: 4)