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Adsolute and conditional convergence of alternating series

  1. Apr 1, 2010 #1
    i have a question regarding adsolute and conditional convergence of alternating series.

    - i know that summation of [ tan(pi/n) ] diverge, but how do we proof it converge conditionally? (ie, (-1)^n tan(pi/n) ]

    can Leibiniz's theorem be used in this case? but tan(pi/2) is infinite?

    any help is appreciated. =D
     
  2. jcsd
  3. Apr 1, 2010 #2

    Dick

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    If you write it as sum n=3 to infinity then you can use the alternating series test. If the series includes n=2 then it would be undefined.
     
  4. Apr 1, 2010 #3
    so alternating series of tan(pi/n) converge conditionally for n>3 only ?
    for n>0 it is diverge?
     
  5. Apr 1, 2010 #4
    Conditional convergence of an alternating series means that it converges but if you take the absolute value it diverges?
     
  6. Apr 1, 2010 #5

    Dick

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    Maybe. Read the fine print in the definition and consult a lawyer. I would prefer to call the case n>0 undefined rather than divergent.
     
  7. Apr 1, 2010 #6

    Dick

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    Well, yes.
     
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