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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


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    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


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    If you mean |r|<1, then yes, the sequence converges to zero.
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