Sum of an infinite series

  • #1

Main Question or Discussion Point

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
 

Answers and Replies

  • #2
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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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