MathDB

37

Part of PEN S Problems

Problems(1)

S 37

Source:

5/25/2007
Let nn and kk are integers with n>0n>0. Prove that −12n∑m=1n−1cot⁡πmnsin⁡2πkmn={kn−⌊kn⌋−12if k∣n0otherwise.-\frac{1}{2n}\sum^{n-1}_{m=1}\cot \frac{\pi m}{n}\sin \frac{2\pi km}{n}= \begin{cases}\tfrac{k}{n}-\lfloor\tfrac{k}{n}\rfloor-\frac12 & \text{if }k|n \\ 0 & \text{otherwise}\end{cases}.
trigonometryfloor functionMiscellaneous Problems