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Convergence/Divergence of this sequence

  1. Apr 21, 2009 #1
    Hello,

    I am trying to find if this sequence is converging or diverging:

    http://img9.imageshack.us/img9/623/72142860.gif [Broken]

    Here is my work, but I highly doubt it because it is based on intuition:
    http://img4.imageshack.us/img4/3589/54428513.gif [Broken]
    Since the first limit diverges and the second limit is not equal to 0, then the sequence diverges.
    Does anyone have a better, systematic way of dealing with this sequence and any other sign alternating sequence with (-1)^n

    Thank you
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 21, 2009 #2

    tiny-tim

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    Hello fishingspree2! :smile:
    [/URL]

    Do you mean the sum, ∑ of that?

    Hint: try subtracting one term from the next … that'll give you a sum of positive terms. :wink:
     
    Last edited by a moderator: May 4, 2017
  4. Apr 21, 2009 #3
  5. Apr 21, 2009 #4

    tiny-tim

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    oooh sorry :redface:

    i was confused by the square brackets

    (i wish the latex was back :frown:)

    in that case …
    Why do you doubt it … that's fine! :biggrin:

    Just tune it slightly by saying that the even terms converge to 2, and the odd terms converge to -2, so clearly it has no limit. :smile:
     
    Last edited by a moderator: May 4, 2017
  6. Apr 21, 2009 #5
    thank you tiny-tim :)
     
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