Question Number 155403 by BHOOPENDRA last updated on 30/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155399 by 0731619 last updated on 30/Sep/21 Answered by TheHoneyCat last updated on 30/Sep/21 $$\mathrm{lim}_{\mathrm{n}\rightarrow+\infty\:} \underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}=+\infty \\ $$$$\mathrm{hence}\:\frac{\mathrm{1}}{\Sigma\frac{\mathrm{1}}{{n}}}\:\underset{{n}\rightarrow\infty} {\rightarrow}\mathrm{0} \\ $$…
Question Number 24324 by Tinkutara last updated on 15/Nov/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{possible}\:\mathrm{least} \\ $$$$\mathrm{common}\:\mathrm{multiple}\:\left(\mathrm{lcm}\right)\:\mathrm{of}\:\mathrm{twenty}\:\left(\mathrm{not}\right. \\ $$$$\left.\mathrm{necessarily}\:\mathrm{distinct}\right)\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\mathrm{whose}\:\mathrm{sum}\:\mathrm{is}\:\mathrm{801}. \\ $$ Commented by Tinkutara last updated on 16/Nov/17…
Question Number 155393 by cortano last updated on 30/Sep/21 $$\:\:\mid\mid\mathrm{x}−\mathrm{4}\mid−\mathrm{4}\mid\:\geqslant\:\mathrm{4}\: \\ $$ Answered by mr W last updated on 30/Sep/21 $$\mid{x}−\mathrm{4}\mid−\mathrm{4}\geqslant\mathrm{4}\: \\ $$$$\Rightarrow\mid{x}−\mathrm{4}\mid\geqslant\mathrm{8}\: \\ $$$$\Rightarrow{x}−\mathrm{4}\geqslant\mathrm{8}\:{or}\:{x}−\mathrm{4}\leqslant−\mathrm{8}\:…
Question Number 155392 by cortano last updated on 30/Sep/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\left({a}^{{x}+\mathrm{1}} +{b}^{{x}+\mathrm{1}} \right)^{\mathrm{2}} }{{a}+{b}}\right)^{\frac{\mathrm{1}}{{x}}} =\ldots? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89852 by M±th+et£s last updated on 19/Apr/20 Answered by mr W last updated on 19/Apr/20 $${F}_{{n}} =\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\varphi^{{n}} −\psi^{{n}} \right)\:{with} \\ $$$$\varphi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}},\:\psi=\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}=\mathrm{1}−\varphi=−\frac{\mathrm{1}}{\varphi} \\ $$$${x}^{{n}}…
Question Number 155384 by aliyn last updated on 29/Sep/21 $$\boldsymbol{{Solve}}\::\:\boldsymbol{{x}}^{\mathrm{2}} \:−\:\left(\mathrm{5}−\boldsymbol{{i}}\right)\boldsymbol{{x}}\:+\:\left(\mathrm{12}−\mathrm{5}\boldsymbol{{i}}\right)\:=\:\mathrm{0} \\ $$ Commented by aliyn last updated on 29/Sep/21 $$???? \\ $$ Answered by…
Question Number 89848 by 9933039645 last updated on 19/Apr/20 $${Q}\mathrm{1}.\:{If}\:{sin}\theta=\frac{\mathrm{3}}{\mathrm{5}}\:{then}\:{find}\:{the}\:{value}\:{of}\:{tan}\theta+{cot}\theta \\ $$ Commented by mahdi last updated on 19/Apr/20 $$\pm\frac{\mathrm{25}}{\mathrm{12}} \\ $$$$\mathrm{sin}\theta=\frac{\mathrm{3}}{\mathrm{5}}\Rightarrow\mid\mathrm{cos}\theta\mid=\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \theta}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\mathrm{tan}\theta=\frac{\mathrm{sin}\theta}{\mathrm{cos}\theta}=\pm\frac{\mathrm{3}}{\mathrm{4}}\:\:\:\:\:\:\mathrm{cot}\theta=\frac{\mathrm{1}}{\mathrm{tan}\theta}=\pm\frac{\mathrm{4}}{\mathrm{3}}…
Question Number 155386 by mathdanisur last updated on 29/Sep/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{H}_{\boldsymbol{\mathrm{k}}} \right)^{\mathrm{3}} }{\mathrm{2}^{\boldsymbol{\mathrm{k}}} }\:=\:\frac{\mathrm{3}\zeta\left(\mathrm{3}\right)\:+\:\mathrm{ln}^{\mathrm{3}} \mathrm{2}\:+\:\pi^{\mathrm{2}} \mathrm{ln2}}{\mathrm{3}}\:\: \\ $$ Answered by Kamel last…
Question Number 89849 by ajfour last updated on 19/Apr/20 Commented by ajfour last updated on 19/Apr/20 $${Find}\:{maximum}\:{area}\:{of}\:\bigtriangleup{PQR} \\ $$$${in}\:{terms}\:{of}\:{ellipse}\:{parameters}\:{a},{b}. \\ $$$${or}\:\:{find}\:{side}\:{of}\:\bigtriangleup{PQR}\:{when} \\ $$$${it}\:{is}\:{equilateral}. \\ $$…