# Evaluate $\sum_{k=1}^{\infty}\frac{\sin k}{k}$. [duplicate]

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.

## marked as duplicate by Norbert, user641, Brian M. Scott, rschwieb, Jason DeVitoOct 21 '12 at 14:20

• Related: math.stackexchange.com/questions/13490/… (That question is about the series $\sum \frac{\sin kx}k$.) – Martin Sleziak Oct 21 '12 at 8:13
• @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 $x=1$.) – Martin Sleziak Oct 21 '12 at 10:42