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Sum of an infinite series

  1. Nov 16, 2011 #1
    I was doing my math homework when I started thinking about the sums of two infinite series.
    I determined that the sum of the first series [itex]\sum_{n=1}^{\infty} cos(\frac{\pi}{2n}) [/itex] diverges. I could not figure out whether or not the series [itex]\sum_{n=1}^{\infty} sin(\frac{\pi}{2n})[/itex] converges or diverges. I think it diverges but I'm unsure because as n approaches infinity each term in the series approaches zero.
    Any help would be much appreciated. Thank you in advance
     
  2. jcsd
  3. Nov 16, 2011 #2
    Try to do a comparison test. Try to use the inequality:

    [tex]\frac{1}{2}x\leq \sin(x)[/tex]

    which holds for small x.
     
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