Question Number 197935 by Frix last updated on 04/Oct/23 $$\mathrm{Show}\:\mathrm{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left({n}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}\right)!}\:=\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}\pi\sqrt{\mathrm{3}}}{\mathrm{27}} \\ $$ Answered by witcher3 last updated on 05/Oct/23 $$\underset{\mathrm{n}\geqslant\mathrm{1}}…
Question Number 197919 by universe last updated on 04/Oct/23 $$\:\:\:\:\:\:\mathrm{I}_{{m}} \:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\lfloor\mathrm{2}^{{m}} {x}\rfloor}{\mathrm{3}^{{m}} }\:\underset{{n}={m}+\mathrm{1}} {\overset{\infty} {\sum}}\frac{\lfloor\mathrm{2}^{{n}} {x}\rfloor}{\mathrm{3}^{{n}} }\right){dx} \\ $$$$\:\:\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\mathrm{I}\:=\:\:\:\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{I}_{{m}}…
Question Number 197914 by a.lgnaoui last updated on 04/Oct/23 $$\boldsymbol{\mathrm{Determiner}}\:\boldsymbol{\mathrm{la}}\:\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{hachuree}} \\ $$$$\left(\boldsymbol{\mathrm{voir}}\:\:\boldsymbol{\mathrm{figure}}\right) \\ $$$$\:\boldsymbol{\mathrm{BC}}=\mathrm{10}\boldsymbol{\mathrm{cm}}\:\:\:\:\:\measuredangle\boldsymbol{\mathrm{B}}=\mathrm{45}°\:\:\:\:\:\:\measuredangle\boldsymbol{\mathrm{C}}=\mathrm{30}° \\ $$ Commented by a.lgnaoui last updated on 04/Oct/23 Commented by…
Question Number 197920 by cortano12 last updated on 04/Oct/23 Commented by cortano12 last updated on 04/Oct/23 $$\mathrm{if}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{shaded}\:\mathrm{is}\:\mathrm{320}\:\mathrm{cm}^{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{big}\:\mathrm{triangle}.\: \\ $$ Answered by Tokugami last…
Question Number 197922 by cherokeesay last updated on 04/Oct/23 Commented by Frix last updated on 04/Oct/23 $$\mathrm{Question}\:\mathrm{197876} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 197908 by mathlove last updated on 03/Oct/23 $${sin}\mathrm{18}^{°} =? \\ $$ Answered by universe last updated on 03/Oct/23 $$\mathrm{sin}\:\left(\mathrm{36}°+\mathrm{54}°\right)\:=\:\mathrm{sin}\:\mathrm{90}° \\ $$$$\mathrm{36}°\:+\:\mathrm{54}°\:=\:\mathrm{90}°\: \\ $$$${x}\:=\:\mathrm{18}°\:…
Question Number 197906 by mnjuly1970 last updated on 03/Oct/23 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{S}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\Gamma^{\:\mathrm{2}} \left(\:{k}\:\right)}{{k}\:\Gamma\:\left(\mathrm{2}{k}\:\right)}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:−−−− \\ $$ Answered by Dwan last updated on…
Question Number 197880 by universe last updated on 02/Oct/23 $$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{infinite}\:\mathrm{series} \\ $$$$\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}} }\centerdot\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{4}} }\left(\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} \right)\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\centerdot\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{6}} }\left(\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +…+\mathrm{7}^{\mathrm{2}} \right)+…
Question Number 197881 by Abdullahrussell last updated on 02/Oct/23 Commented by Frix last updated on 02/Oct/23 $$\mathrm{2}−\sqrt{\mathrm{3}} \\ $$ Answered by Sutrisno last updated on…
Question Number 197882 by CrispyXYZ last updated on 02/Oct/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{5}{t}^{\mathrm{2}} −\mathrm{8}{t}+\mathrm{5}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right){t}^{\mathrm{2}} −\mathrm{2}{t}+\mathrm{2}−\sqrt{\mathrm{3}}}\:\:\mathrm{where}\:\mathrm{2}−\sqrt{\mathrm{3}}<{t}<\mathrm{2}+\sqrt{\mathrm{3}}. \\ $$ Answered by mr W last updated on 03/Oct/23 $$\frac{\mathrm{5}{t}^{\mathrm{2}}…