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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 $$\pi\:=\:\mathrm{180}°\:=\:\Pi \\ $$$$\pi\:=\:\mathrm{3},\mathrm{141}…\:=\:\pi \\ $$$$\mathrm{Solve}\:\left(\mathrm{find}\:{n}\:\in\:\mathbb{N}\right): \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} \pi\right)}{{k}}\:+\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{k}\centerdot\mathrm{10}^{{n}} {e}\right)}{{k}}\:=\:\mathrm{0} \\ $$$$ \\…

Question-9403

Question Number 9403 by alfat123 last updated on 05/Dec/16 Answered by ridwan balatif last updated on 05/Dec/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{5x}\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{6}} \mathrm{dx}=\mathrm{u}.\mathrm{v}−\int\mathrm{vdu} \\ $$$$\mathrm{misal}:\:\mathrm{u}=\mathrm{5x}\rightarrow\mathrm{du}=\mathrm{5dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{dv}=\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{6}}…

Question-140462

Question Number 140462 by ZiYangLee last updated on 08/May/21 Commented by mr W last updated on 08/May/21 $${T}_{{n}} ={ar}^{{n}−\mathrm{1}} \\ $$$$\frac{{T}_{{n}+\mathrm{4}} −{T}_{{n}+\mathrm{2}} }{{T}_{{n}+\mathrm{1}} }=\frac{{ar}^{{n}+\mathrm{3}} −{ar}^{{n}+\mathrm{1}}…

I-was-able-to-discover-the-conditions-for-the-sum-of-two-irrational-numbers-be-an-integer-and-the-conditions-for-the-sum-be-a-finite-decimal-But-I-can-not-do-the-same-for-periodic-tithe-Someone-can-

Question Number 9372 by geovane10math last updated on 03/Dec/16 $$\mathrm{I}\:\mathrm{was}\:\mathrm{able}\:\mathrm{to}\:\mathrm{discover}\:\mathrm{the}\:\mathrm{conditions}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{irrational}\:\mathrm{numbers}\:\mathrm{be}\:\mathrm{an} \\ $$$$\mathrm{integer}\:\mathrm{and}\:\mathrm{the}\:\mathrm{conditions}\:\mathrm{for}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{be}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{decimal}. \\ $$$$\mathrm{But}\:\mathrm{I}\:\mathrm{can}\:\mathrm{not}\:\mathrm{do}\:\mathrm{the}\:\mathrm{same}\:\mathrm{for}\:\mathrm{periodic} \\ $$$$\mathrm{tithe}. \\ $$$$\mathrm{Someone}\:\mathrm{can}\:\mathrm{help}\:\mathrm{me},\:\mathrm{please}? \\ $$$$ \\…