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Author: Tinku Tara

Find-a-x-integer-k-1-sin-2-kxpi-k-k-1-sin-2-kxe-k-0-Where-represents-180-represents-3-14159265358-

Question Number 9727 by geovane10math last updated on 29/Dec/16 $$\mathrm{Find}\:\mathrm{a}\:\boldsymbol{{x}}\:{integer}: \\ $$$$\left[\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{kx}\pi\right)}{{k}}\right]\:+\:\left[\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{kxe}\right)}{{k}}\right]\:=\:\mathrm{0}\: \\ $$$$ \\ $$$$\boldsymbol{\mathrm{Where}}: \\ $$$$\boldsymbol{\Pi}\:\mathrm{represents}\:\mathrm{180}°\:; \\ $$$$\boldsymbol{\pi}\:\mathrm{represents}\:\mathrm{3},\mathrm{14159265358}…\:. \\…

n-1-1-n-3-4n-n-

Question Number 140798 by Dwaipayan Shikari last updated on 12/May/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{3}} \begin{pmatrix}{\mathrm{4}{n}}\\{{n}}\end{pmatrix}} \\ $$ Commented by john_santu last updated on 14/May/21 $$\:\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}} \\…

Let-A-2-4-6-7-8-9-B-1-3-5-6-10-and-C-x-3x-6-0-or-2x-6-0-Find-a-A-B-b-is-A-B-C-A-B-C-

Question Number 75257 by must1987 last updated on 09/Dec/19 $${Let}\:{A}=\left\{\mathrm{2},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9}\right\} \\ $$$${B}=\left\{\mathrm{1},\mathrm{3},\mathrm{5},\mathrm{6},\mathrm{10}\right\}\:{and} \\ $$$${C}=\left\{{x}:\mathrm{3}{x}+\mathrm{6}=\mathrm{0}\:{or}\:\mathrm{2}{x}+\mathrm{6}=\mathrm{0}\right\}.{Find} \\ $$$${a}.\:{A}\cup{B}. \\ $$$${b}.\:{is}\left({A}\cup{B}\right)\cup{C}={A}\cup\left({B}\cup{C}\right)? \\ $$ Answered by 21042004 last updated…

Question-75254

Question Number 75254 by must1987 last updated on 09/Dec/19 Answered by 21042004 last updated on 09/Dec/19 $$\mathrm{1}.\:{B}=\left\{\mathrm{1},\mathrm{2},\mathrm{6}\right\} \\ $$$$\left.\mathrm{2}.\:{a}\right)\:{A}\cup{B}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\} \\ $$$$\left.\:\:\:\:\:{b}\right)\:{Yes} \\ $$$$\left.\mathrm{3}.\:{a}\right)\:{A}'=\left\{\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{9}\right\} \\ $$$$\left.\:\:\:\:\:{b}\right)\:{A}\cap{A}'=\varnothing…