Question Number 88372 by mr W last updated on 10/Apr/20 $${There}\:{are}\:{four}\:{boxes},\:{each}\:{of}\:{them} \\ $$$${contains}\:{exactly}\:{the}\:{same}\:{numbers}: \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},…,{n}. \\ $$$${Four}\:{different}\:{numbers}\:{are}\:{drawn} \\ $$$${from}\:{the}\:{boxes}\:{and}\:{multiplicated} \\ $$$${with}\:{each}\:{other}\:{to}\:{get}\:{a}\:{product}. \\ $$$${What}'{s}\:{the}\:{sum}\:{of}\:{all}\:{products}? \\ $$$$\underset{{a}\neq{b}\neq{c}\neq{d}}…
Question Number 153903 by mathdanisur last updated on 11/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 153897 by mathdanisur last updated on 11/Sep/21 $$\mathrm{Denote}\:\:\mathrm{x}_{\boldsymbol{\mathrm{n}}} \:\:\mathrm{is}\:\mathrm{the}\:\mathrm{unique}\:\mathrm{positive}\:\mathrm{root} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{x}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \:+\:…\:\mathrm{x}\:=\:\mathrm{n}\:+\:\mathrm{2} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{x}_{\boldsymbol{\mathrm{n}}} \right)\:\mathrm{converges} \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number}.\:\mathrm{Find}\:\mathrm{that} \\ $$$$\mathrm{limit}. \\…
Question Number 88360 by jagoll last updated on 10/Apr/20 $$\frac{\mathrm{e}}{\:\sqrt{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{3}\:\:}]{\mathrm{e}}}{\:\sqrt[{\mathrm{4}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{5}\:\:}]{\mathrm{e}}}{\:\sqrt[{\mathrm{6}\:\:}]{\mathrm{e}}}\:×\:\frac{\sqrt[{\mathrm{7}\:\:}]{\mathrm{e}}}{\:\sqrt[{\mathrm{8}\:\:}]{\mathrm{e}}}×…=? \\ $$ Commented by john santu last updated on 10/Apr/20 $$=\:{e}^{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{6}}+…} \\ $$$$\left[\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}\right)\:=\:\mathrm{x}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{x}^{\mathrm{4}}…
Question Number 153899 by mathdanisur last updated on 11/Sep/21 $$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{there}\:\mathrm{exists}\:\:\mathrm{2016} \\ $$$$\mathrm{distinct}\:\mathrm{prime}\:\mathrm{numbers}\:\:\mathrm{p}_{\mathrm{1}} ,\mathrm{p}_{\mathrm{2}} ,…,\mathrm{p}_{\mathrm{2016}} \\ $$$$\mathrm{and}\:\mathrm{positive}\:\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{i}}=\mathrm{1}} {\overset{\mathrm{2016}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{p}_{\boldsymbol{\mathrm{i}}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} } \\ $$…
Question Number 153898 by mathdanisur last updated on 11/Sep/21 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{functions}\:\:\mathrm{f}:\mathrm{Q}\rightarrow\mathrm{Q}\:\:\mathrm{satisfying} \\ $$$$\mathrm{these}\:\mathrm{followong}\:\mathrm{conditions}\:\mathrm{for}\:\mathrm{all}\:\boldsymbol{\mathrm{x}}\in\mathrm{Q} \\ $$$$\mathrm{1}.\:\mathrm{f}\left(\mathrm{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{1} \\ $$$$\mathrm{2}.\:\mathrm{f}\left(\mathrm{x}^{\mathrm{3}} \right)\:=\:\mathrm{f}^{\:\mathrm{3}} \left(\mathrm{x}\right) \\ $$ Answered by talminator2856791 last updated…
Question Number 153895 by eman_64 last updated on 11/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 153867 by mathdanisur last updated on 11/Sep/21 Commented by mathdanisur last updated on 11/Sep/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{real}\:\mathrm{roots} \\ $$ Commented by Tawa11 last updated on…
Question Number 153864 by liberty last updated on 11/Sep/21 Commented by MJS_new last updated on 11/Sep/21 $$\mathrm{1}\:\mathrm{equation}\:/\:\mathrm{3}\:\mathrm{unknown}\:??? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 153870 by physicstutes last updated on 11/Sep/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\frac{\mathrm{5}}{{f}\left(\theta\right)+\mathrm{3}}\:\mathrm{where}\:{f}\left(\theta\right)=\mathrm{8cos}\:\theta−\mathrm{15}\:\mathrm{sin}\:\theta \\ $$ Commented by mr W last updated on 12/Sep/21 $${there}\:{are}\:{no}\:{minimum}\:{and}\:{no} \\ $$$${maximum}.\:{there}\:{are}\:{only}\:{local}\:…