I want to show $\dfrac{1}{\pi}\sum_{m=1}^{\infty}\dfrac{\sin(2\pi mx)}{m}= -(x-[x]-\dfrac{1}{2})$,when x is not an integer,where [x] denotes greatest integer function . Could you please give any suggestion how to approach?? Thanks
2026-03-30 05:25:11.1774848311
Closed form of an expression.
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