0
$\begingroup$

Possible Duplicate:
Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$

Evaluate $\displaystyle\sum_{k=1}^{\infty}\frac{\sin k}{k}$.

By a calculator, I'm convinced that it convergents, but I'm not sure how to calculate it. Please help. Thank you.

  • 2
    http://math.stackexchange.com/a/183471/248752012-10-21
  • 0
    Related: http://math.stackexchange.com/questions/13490/proving-that-the-sequence-f-nx-sum-limits-k-1n-frac-sinkxk-is (That question is about the series $\sum \frac{\sin kx}k$.)2012-10-21
  • 0
    Here. http://math.stackexchange.com/questions/161960/sum-inequality-sum-k-1n-frac-sin-kk-le-pi-12012-10-21
  • 0
    It’s actually @Martin’s link that answers the question.2012-10-21
  • 0
    @Brian That is, of course, true. But I am always in doubt about closing questions as duplicates, when one of them is a special case of the other one. (I admit that in this case it seems very improbable that there would be some very special method for $x=1$.)2012-10-21
  • 0
    @Martin: I was just pointing that out for the benefit of anyone who might be considering voting to close. As it happens, all three who have so far done so have cited that answer.2012-10-21

0 Answers 0