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for-a-gt-0-and-b-gt-a-2-verify-the-follwing-claim-n-1-n-a-a-1-a-2-a-n-1-b-b-1-b-2-b-n-1-a-b-1-b-a-1-b-a-2-

Question Number 78456 by arkanmath7@gmail.com last updated on 17/Jan/20 $${for}\:{a}>\mathrm{0}\:{and}\:{b}>{a}+\mathrm{2}\:,\:\:{verify}\:{the}\:{follwing}\: \\ $$$${claim}: \\ $$$$\:\:\:\sum_{{n}=\mathrm{1}} ^{\:\:\infty} \:{n}\:\frac{{a}\left({a}+\mathrm{1}\right)\left({a}+\mathrm{2}\right)…\left({a}+{n}−\mathrm{1}\right)}{{b}\left({b}+\mathrm{1}\right)\left({b}+\mathrm{2}\right)…\left({b}+{n}−\mathrm{1}\right)}\:=\frac{{a}\left({b}−\mathrm{1}\right)}{\left({b}−{a}−\mathrm{1}\right)\left({b}−{a}−\mathrm{2}\right)} \\ $$ Answered by mind is power last updated…

Given-that-is-a-complex-number-7-1-1-find-the-value-of-1-2-3-4-5-6-

Question Number 143970 by ZiYangLee last updated on 20/Jun/21 $$\mathrm{Given}\:\mathrm{that}\:\omega\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}, \\ $$$$\omega^{\mathrm{7}} =\mathrm{1},\:\omega\neq\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\omega^{\mathrm{1}} +\omega^{\mathrm{2}} +\omega^{\mathrm{3}} +\omega^{\mathrm{4}} +\omega^{\mathrm{5}} +\omega^{\mathrm{6}} . \\ $$ Answered by…

Question-143965

Question Number 143965 by Khalmohmmad last updated on 20/Jun/21 Commented by Canebulok last updated on 20/Jun/21 $$\boldsymbol{{Solution}}: \\ $$$$\Rightarrow\:\frac{{log}\left({x}\right)}{{log}\left(\mathrm{3}\right)}\:+\:\frac{{log}\left(\mathrm{5}\right)}{{log}\left({x}\right)}\:=\:\mathrm{0} \\ $$$$\Rightarrow\:{log}\left({x}\right)^{\mathrm{2}} \:+\:{log}\left(\mathrm{5}\right){log}\left(\mathrm{3}\right)\:=\:\mathrm{0} \\ $$$$\: \\…

x-1-and-x-2-are-solutions-of-equality-cos-pix-pi-6-sin-pix-pi-6-1-2-3-0-x-12-Find-the-value-of-x-1-x-2-

Question Number 143964 by naka3546 last updated on 20/Jun/21 $${x}_{\mathrm{1}} \:{and}\:\:{x}_{\mathrm{2}} \:\:{are}\:\:{solutions}\:\:{of}\:\:{equality}\:: \\ $$$$\:\:\mathrm{cos}\:\left(\frac{\pi{x}+\pi}{\mathrm{6}}\right)\:−\:\mathrm{sin}\:\left(\frac{\pi{x}−\pi}{\mathrm{6}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\sqrt{\mathrm{3}}\:\:\:,\:\:\:\mathrm{0}\:\leqslant\:{x}\:\leqslant\:\mathrm{12} \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{x}_{\mathrm{1}} +\:{x}_{\mathrm{2}} \:. \\ $$ Commented by Canebulok last updated…

A-x-ln-y-x-y-ln-z-x-z-ln-x-y-

Question Number 143963 by SOMEDAVONG last updated on 20/Jun/21 $$\mathrm{A}=\mathrm{x}^{\mathrm{ln}\frac{\mathrm{y}}{\mathrm{x}}} .\mathrm{y}^{\mathrm{ln}\frac{\mathrm{z}}{\mathrm{x}}} .\mathrm{z}^{\mathrm{ln}\frac{\mathrm{x}}{\mathrm{y}}} =?? \\ $$ Answered by Olaf_Thorendsen last updated on 20/Jun/21 $$\mathrm{A}\:=\:{x}^{\mathrm{ln}\frac{{y}}{{x}}} {y}^{\mathrm{ln}\frac{{z}}{{x}}} {z}^{\mathrm{ln}\frac{{x}}{{y}}}…