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Converge, absolutely or conditionally?

  1. Jan 24, 2007 #1
    1. The problem statement, all variables and given/known data

    does it converge absolutely, converge conditionally, or diverge?

    heres the equation: http://img219.imageshack.us/img219/4645/untitled29fy.jpg

    2. Relevant equations


    3. The attempt at a solution

    looks like the sin equation converges to zero.

    i think this is an alternating series, but i'm not sure if this part converges or diverges?

    thanks for any help here.
  2. jcsd
  3. Jan 24, 2007 #2

    Gib Z

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    Yep, The terms converge to zero, and it converges absolutely, and therfore also with the alternating series.
  4. Jan 24, 2007 #3
    Great, thanks again.

    ..also, the alternating series must approach 0, in order to converge right?

    ..and, in this problem, sin(pi/anything) will always be 0, correct?
    Last edited: Jan 24, 2007
  5. Jan 24, 2007 #4

    Gib Z

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    Ahh no, if anything was a constant that it wont be zero.
  6. Jan 24, 2007 #5


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    Science Advisor
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    No ... but sin(pi*n) is always 0 when n is an integer. Maybe that's what you were thinking of (though it doesn't seem relevant to this question).
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