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Question-122377

Question Number 122377 by aristarque last updated on 16/Nov/20 Commented by Dwaipayan Shikari last updated on 16/Nov/20 $$\sqrt[{\mathrm{3}}]{\mathrm{54}\sqrt{\mathrm{3}}+\mathrm{41}\sqrt{\mathrm{5}}}\:=\sqrt[{\mathrm{3}}]{\left(\mathrm{2}\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}\right)^{\mathrm{3}} } \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{54}\sqrt{\mathrm{3}}−\mathrm{41}\sqrt{\mathrm{5}}}=\sqrt{\left(\mathrm{2}\sqrt{\mathrm{3}}−\sqrt{\mathrm{5}}\right)^{\mathrm{3}} } \\ $$$${A}=\frac{\mathrm{2}\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}+\mathrm{2}\sqrt{\mathrm{3}}−\sqrt{\mathrm{5}}}{\:\sqrt{\mathrm{3}}}=\mathrm{4} \\…

1-9-1-4-4-17-1-5-4-8-4-25-1-5-9-4-8-12-4-pi-2-2-2-3-4-

Question Number 122317 by Dwaipayan Shikari last updated on 15/Nov/20 $$\mathrm{1}+\mathrm{9}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} +\mathrm{17}\left(\frac{\mathrm{1}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}\right)^{\mathrm{4}} +\mathrm{25}\left(\frac{\mathrm{1}.\mathrm{5}.\mathrm{9}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}\right)^{\mathrm{4}} +…=\frac{\pi}{\mathrm{2}\sqrt{\mathrm{2}}\left(\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

if-x-y-show-that-x-y-x-y-iff-xy-0-

Question Number 56775 by zambolly19 last updated on 23/Mar/19 $${if}\:{x},{y}\backepsilon\Re,{show}\:{that}\:\mid{x}+{y}\mid=\mid{x}\mid+\mid{y}\mid\:{iff}\:{xy}\geqslant\mathrm{0} \\ $$ Commented by maxmathsup by imad last updated on 23/Mar/19 $${we}\:{have}\:\mid{x}+{y}\mid^{\mathrm{2}} −\left(\mid{x}\mid+\mid{y}\mid\right)^{\mathrm{2}} \:={x}^{\mathrm{2}} +\mathrm{2}{xy}+{y}^{\mathrm{2}}…

log1-1-log3-3-log5-5-log7-7-C-pi-4-2-1-2-log-2pi-1-1-1-3-C-Eulerian-constant-

Question Number 122303 by Dwaipayan Shikari last updated on 15/Nov/20 $$\frac{{log}\mathrm{1}}{\:\sqrt{\mathrm{1}}}−\frac{{log}\mathrm{3}}{\:\sqrt{\mathrm{3}}}+\frac{{log}\mathrm{5}}{\:\sqrt{\mathrm{5}}}−\frac{{log}\mathrm{7}}{\:\sqrt{\mathrm{7}}}+..{C}=\left(\frac{\pi}{\mathrm{4}}−\frac{\gamma}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}{log}\left(\mathrm{2}\pi\right)\right)\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+..{C}\right) \\ $$$$\gamma\:=\mathscr{E}{ulerian}\:{constant} \\ $$ Commented by rs4089 last updated on 15/Nov/20 $${i}\:{think}\:{its}\:{expansion}\:{is}\:{given}\:{by}\:{indian}\:{mathematician}\:\:{srinivasa}\:{ramanujan}\:{to}\:{profecer}\:{g}.{h}.\:{hardy}\:. \\ $$…