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pi-180-pi-3-141-pi-Solve-find-n-N-k-1-sin-2-k-10-n-pi-k-k-1-sin-2-k-10-n-e-k-0-




Question Number 9407 by geovane10math last updated on 06/Dec/16
π = 180° = Π  π = 3,141... = π  Solve (find n ∈ N):  Σ_(k=1) ^∞ ((sin(2Πk∙10^n π))/k) + Σ_(k=1) ^∞ ((sin(2Πk∙10^n e))/k) = 0
$$\pi\:=\:\mathrm{180}°\:=\:\Pi \\ $$$$\pi\:=\:\mathrm{3},\mathrm{141}…\:=\:\pi \\ $$$$\mathrm{Solve}\:\left(\mathrm{find}\:{n}\:\in\:\mathbb{N}\right): \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} \pi\right)}{{k}}\:+\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} {e}\right)}{{k}}\:=\:\mathrm{0} \\ $$$$ \\ $$

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