trigonometry limit's proof – math.stackexchange.com

trigonometry limit's proof – math.stackexchange.com

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How to prove that $$\lim_{x\to0}\frac{\sin(x)+\sin(2x)+\cdots+\sin(kx)}{x}=\frac{k(k+1)}{2}$$ I tried to split up the fraction and multiple-divide every new fraction with its $x$ factor but didn't ...

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