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Series question

  1. Feb 4, 2008 #1
    does the series from 1 to infinity of [tex]\sum[/tex](1 - (2/n))^3n convegre or diverge.

    i've tried almost all the tests and cant figure it out....
     
  2. jcsd
  3. Feb 4, 2008 #2
  4. Feb 4, 2008 #3

    quasar987

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    Have you even tried the simplest test of them all? Does the argument of the series goes to 0 as n increases without bounds?
     
  5. Feb 4, 2008 #4
    i've tried the root test. does not work. meaning it's inconclusive.

    and i dont understand your question.
    "Does the argument of the series goes to 0 as n increases without bounds?"
    are you saying do the terms get closer to zero? yes.
     
  6. Feb 4, 2008 #5
    if you can hint me to what test i should use maybe i can figure it out.
     
  7. Feb 5, 2008 #6

    quasar987

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    Yes, this is what I was asking, but 'yes' is not the answer I had in mind!

    Remember that

    [tex]\left(1+\frac{1}{n}\right)^n \rightarrow e[/tex]

    !
     
  8. Feb 5, 2008 #7
    and therefore by the divergence test...the series diverges?
     
  9. Feb 5, 2008 #8

    quasar987

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    I was merely pointing out a sequence that behaves like the argument of your series and that does not go to 0.

    However, you can cleverly manipulate the identity

    [tex]\left(1+\frac{1}{n}\right)^n \rightarrow e[/tex]

    to find the precise value of the limit you're interested in.
     
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