Question Number 114023 by Khalmohmmad last updated on 16/Sep/20 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\propto} {\sum}}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{1}}=? \\ $$ Commented by Dwaipayan Shikari last updated on 16/Sep/20 $${Diverges} \\…
Question Number 48482 by ajfour last updated on 24/Nov/18 $$\left({at}−{h}\right)^{\mathrm{2}} +\left(\frac{{a}}{{t}}−{k}\right)^{\mathrm{2}} ={R}^{\:\mathrm{2}} \\ $$$${where}\:\:\:{a},\:{h},\:{k},\:{R}\:{are}\:{constants}. \\ $$$${Then}\:{find}\: \\ $$$$\:\:\:{s}^{\mathrm{2}} \:=\left({t}_{\mathrm{1}} −{t}_{\mathrm{2}} \right)^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{t}_{\mathrm{1}} ^{\mathrm{2}} {t}_{\mathrm{2}} ^{\mathrm{2}}…
Question Number 113997 by Aina Samuel Temidayo last updated on 16/Sep/20 Answered by bobhans last updated on 16/Sep/20 $${consider}\::\:\sqrt{\mathrm{2}}\:+\sqrt[{\mathrm{4}}]{\mathrm{2}}\:+\mathrm{1}\:=\:\left(\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{1}.\left(\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)+\mathrm{1}^{\mathrm{2}} \:=\:\frac{\left(\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)^{\mathrm{3}} −\mathrm{1}^{\mathrm{3}} }{\:\sqrt[{\mathrm{4}}]{\mathrm{2}}−\mathrm{1}} \\ $$$${then}\:\frac{\mathrm{7}}{\left(\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 113996 by Aina Samuel Temidayo last updated on 16/Sep/20 Commented by MJS_new last updated on 16/Sep/20 $$\frac{\mathrm{ln}\:\frac{\mathrm{81}}{\mathrm{8}}}{\mathrm{2ln}\:\frac{\mathrm{9}}{\mathrm{2}}}=\frac{\mathrm{ln}\:\sqrt{\frac{\mathrm{81}}{\mathrm{8}}}}{\mathrm{ln}\:\frac{\mathrm{9}}{\mathrm{2}}}=\frac{\mathrm{ln}\:\frac{\mathrm{9}}{\:\sqrt{\mathrm{8}}}}{\mathrm{ln}\:\frac{\mathrm{9}}{\mathrm{2}}}=\mathrm{log}_{\frac{\mathrm{9}}{\mathrm{2}}} \frac{\mathrm{9}}{\:\sqrt{\mathrm{8}}} \\ $$ Answered by bobhans…
Question Number 179529 by mathlove last updated on 30/Oct/22 $$\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{x}} +\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} =\mathrm{4}\:\:\:\:\:\:{x}=? \\ $$ Answered by mr W last updated on 30/Oct/22 $$\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)=\mathrm{2}^{\mathrm{2}} −\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} =\mathrm{4}−\mathrm{3}=\mathrm{1}…
Question Number 48447 by rahul 19 last updated on 24/Nov/18 $${Find}\:{the}\:{sum}\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\:^{\mathrm{20}} {C}_{{k}} \:. \\ $$ Commented by rahul 19 last updated on 24/Nov/18…
Question Number 179517 by cortano1 last updated on 30/Oct/22 $$\:\mathrm{22}!\:\equiv\:\mathrm{x}\:\left(\mathrm{mod}\:\mathrm{2024}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 179518 by mathlove last updated on 30/Oct/22 $${a}−\frac{\mathrm{1}}{{b}}=\mathrm{2}{cos}\frac{\mathrm{2}\pi}{\mathrm{13}} \\ $$$${b}−\frac{\mathrm{1}}{{c}}=\mathrm{2}{cos}\frac{\mathrm{6}\pi}{\mathrm{13}} \\ $$$${c}−\frac{\mathrm{1}}{{a}}=\mathrm{2}{cos}\frac{\mathrm{8}\pi}{\mathrm{13}}\:\:\:\:\:\:{prove}\:{that} \\ $$$$\left({abc}\right)^{\mathrm{5}} −\frac{\mathrm{1}}{\left({abc}\right)^{\mathrm{5}} }=\mathrm{11} \\ $$ Commented by mr W last…
Question Number 48443 by rahul 19 last updated on 24/Nov/18 $${Coefficient}\:{of}\:{x}^{\mathrm{4}} \:{in}\:\left(\mathrm{2}−{x}+\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{6}} =? \\ $$ Commented by rahul 19 last updated on 24/Nov/18 $${Do}\:{by}\:{multinomial}\:{expansions}….…
Question Number 113975 by I want to learn more last updated on 16/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}:\:\:\:\mathrm{1},\:\:\mathrm{0},\:\:−\:\mathrm{1},\:\:\mathrm{0},\:\:\mathrm{1},\:\:\mathrm{0},\:\:−\:\mathrm{1},\:\:\mathrm{0},\:\:… \\ $$ Answered by Olaf last updated on 16/Sep/20 $${u}_{{n}} \:=\:\mathrm{cos}\left({n}\frac{\pi}{\mathrm{2}}\right)…