Question Number 205580 by universe last updated on 25/Mar/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)…\left(\mathrm{4}{n}+\mathrm{1}\right)}{\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}+\mathrm{2}\right)…\left(\mathrm{4}{n}\right)}\:\:=\:\:? \\ $$ Commented by lepuissantcedricjunior last updated on 26/Mar/24 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{1}\right)×\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{3}\right)×…×\left(\mathrm{4}\boldsymbol{{n}}+\mathrm{1}\right)}{\left(\mathrm{2}\boldsymbol{{n}}\right)×\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{2}\right)×..×\left(\mathrm{4}\boldsymbol{{n}}\right)} \\ $$$$=\underset{\boldsymbol{{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{2}\boldsymbol{{n}}\right)\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{1}\right)\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{2}\right)…\left(\mathrm{4}\boldsymbol{{n}}\right)\left(\mathrm{4}\boldsymbol{{n}}+\mathrm{1}\right)}{\left[\left(\mathrm{2}\boldsymbol{{n}}\right)\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{2}\right)….\left(\mathrm{4}\boldsymbol{{n}}\right)\right]^{\mathrm{2}}…
Question Number 205614 by mr W last updated on 25/Mar/24 Answered by A5T last updated on 25/Mar/24 Commented by A5T last updated on 25/Mar/24 $$\frac{{sin}\left(\angle{CFB}\right)}{\mathrm{1}}=\frac{{sin}\mathrm{90}=\mathrm{1}}{\:\sqrt{\mathrm{0}.\mathrm{5}^{\mathrm{2}}…
Question Number 205577 by BaliramKumar last updated on 25/Mar/24 $$\mathrm{is}\:\infty\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}? \\ $$ Commented by mr W last updated on 25/Mar/24 $${it}\:{is}\:{only}\:{a}\:{symbol}.\:{it}\:{may}\:{have}\:\: \\ $$$${different}\:{meanings}\:{depending}\:{on}\: \\ $$$${in}\:{which}\:{context}\:{it}\:{is}\:{used}.\:…
Question Number 205607 by SANOGO last updated on 25/Mar/24 $${soit}\:{H}\:{espace}\:{de}\:{Hilbert} \\ $$$${montrez}\:{que}: \\ $$$${d}\left({x},\left\{{a}\right\}\right)^{\lfloor} \:=\:\frac{\mid<{x},{a}>\mid}{\mid\mid{a}\mid\mid} \\ $$ Answered by Berbere last updated on 25/Mar/24 $$\frac{{a}}{\mid{a}\mid},{a}_{\mathrm{2}}…
Question Number 205551 by aba last updated on 24/Mar/24 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{into}\:\mathrm{cycles} \\ $$$$\mathrm{with}\:\mathrm{disjoints}\:\mathrm{support}\:\mathrm{of}\:\mathrm{c}^{\mathrm{k}} ,\:\mathrm{where}\:\mathrm{c}=\left(\mathrm{123}…\mathrm{n}\right)\:? \\ $$ Answered by TheHoneyCat last updated on 01/Apr/24 $$\mathrm{please}\:\mathrm{don}'\mathrm{t}\:\mathrm{re}−\mathrm{post}\:\mathrm{your}\:\mathrm{questions}. \\ $$$$\mathrm{especially}\:\mathrm{a}\:\mathrm{single}\:\mathrm{day}\:\mathrm{after}……
Question Number 205535 by cortano12 last updated on 24/Mar/24 Answered by A5T last updated on 24/Mar/24 Commented by A5T last updated on 24/Mar/24 $$\frac{{sin}\mathrm{90}=\mathrm{1}}{{BC}}=\frac{{sin}\left(\mathrm{90}−\theta\right)={cos}\theta}{{AB}}\Rightarrow{AB}={BCcos}\theta \\…
Question Number 205545 by Abdullahrussell last updated on 24/Mar/24 Commented by mr W last updated on 24/Mar/24 $$=\mathrm{768612}\:? \\ $$ Answered by A5T last updated…
Question Number 205562 by mr W last updated on 24/Mar/24 Answered by A5T last updated on 24/Mar/24 Commented by A5T last updated on 24/Mar/24 $${CE}=\sqrt{\mathrm{2}{r}^{\mathrm{2}}…
Question Number 205574 by Red1ight last updated on 24/Mar/24 $${S}=\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}… \\ $$$${S}=? \\ $$ Commented by Frix last updated on 25/Mar/24 $${S}=\frac{\mathrm{1}}{\mathrm{e}} \\ $$ Answered…
Question Number 205558 by universe last updated on 24/Mar/24 $$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{4}\theta\:}{\mathrm{sin}^{\mathrm{2}} \theta\:}{d}\theta\:\:=\:\:\:? \\ $$ Answered by Berbere last updated on 24/Mar/24 $${sin}^{\mathrm{2}} \left(\mathrm{4}{x}\right)=\mathrm{4}{sin}^{\mathrm{2}}…