Question Number 196674 by Erico last updated on 29/Aug/23 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} +\underset{\mathrm{p}=\mathrm{2}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{p}} \mathrm{pln}\left(\frac{\mathrm{p}+\mathrm{1}}{\mathrm{p}−\mathrm{1}}\right)=\mathrm{ln}\left(\pi\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 196460 by peter frank last updated on 25/Aug/23 Commented by mr W last updated on 25/Aug/23 $${question}\:{is}\:{not}\:{clear}.\: \\ $$$${t}_{\mathrm{1}} ,{t}_{\mathrm{2}} ,{t}_{\mathrm{3}} \:{are}\:{three}\:{points}.\:{what}\:{do}\:{you} \\…
Question Number 196395 by Amidip last updated on 24/Aug/23 Commented by mr W last updated on 24/Aug/23 $${what}'{s}\:{your}\:{question}? \\ $$ Terms of Service Privacy Policy…
Question Number 196304 by cortano12 last updated on 22/Aug/23 Answered by a.lgnaoui last updated on 24/Aug/23 $$\:\boldsymbol{\mathrm{S}}=\mathrm{shaded}\:\mathrm{Area} \\ $$$$\boldsymbol{\mathrm{S}}\mathrm{1}=\mathrm{Arc}\left(\mathrm{AMC}\right)\:\:\:\boldsymbol{\mathrm{S}}\mathrm{2}=\mathrm{Arc}\left(\mathrm{OBD}\right) \\ $$$$\:\boldsymbol{\mathrm{S}}=\boldsymbol{\mathrm{S}}\left(\boldsymbol{\mathrm{ABCD}}\right)−\boldsymbol{\mathrm{S}}\mathrm{1}+\boldsymbol{\mathrm{S}}\mathrm{2} \\ $$$$\bullet\boldsymbol{\mathrm{Calcul}}\:\boldsymbol{\mathrm{de}}\:\boldsymbol{\mathrm{S}}\left(\mathrm{ABCD}\right) \\ $$$$\:\:\mathrm{OBsin}\:\mathrm{30}=\mathrm{OAsin}\:\mathrm{45}\Rightarrow\:\:\boldsymbol{\mathrm{OA}}=\mathrm{5}\sqrt{\mathrm{2}}\:…
Question Number 196321 by sniper237 last updated on 22/Aug/23 $$\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:{sin}\left(\mathrm{2}\pi\sqrt{{n}^{\mathrm{2}} +\mathrm{1}\:}\:\right)\:=\:\mathrm{0} \\ $$$$\:\:\:\:\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:\:{arg}\left({n}^{\mathrm{2}} +{n}+\mathrm{1}+{i}\right)\:=\:\mathrm{0} \\ $$ Answered by witcher3 last updated on 22/Aug/23…
Question Number 194821 by sniper237 last updated on 16/Jul/23 $${M}\:{a}\:{inside}\:{poin}\:{in}\:\:\Delta{ABC}. \\ $$$${M}\:=\:{bar}\:\left\{\left({A},\:{area}\left({MBC}\right)\right),\:\left({B},\:{area}\left({MAC}\right)\right),\left({C},{area}\left({MAB}\right)\right)\right\} \\ $$ Commented by mr W last updated on 16/Jul/23 $${what}\:{do}\:{mean}\:{with}\:\left({A},\:{area}\left({MBC}\right)\right)? \\ $$$${what}\:{do}\:{mean}\:{with}\:{bar}\:\left\{{X},\:{Y},\:{Z}\right\}?…
Question Number 194301 by a.lgnaoui last updated on 02/Jul/23 $$\boldsymbol{\mathrm{Resolution}}\:\boldsymbol{\mathrm{de}}\:\boldsymbol{\mathrm{l}}\:\boldsymbol{\mathrm{exercice}}\:\boldsymbol{\mathrm{du}}\:\mathrm{28}.\mathrm{6}.\mathrm{23} \\ $$$$\:\:\left({env}\mathrm{o}{ye}\:{par}\:{universe}\:\right) \\ $$$$\boldsymbol{{Q}}\mathrm{194116} \\ $$$$ \\ $$ Answered by a.lgnaoui last updated on 02/Jul/23…
Question Number 194131 by cortano12 last updated on 28/Jun/23 Commented by BaliramKumar last updated on 28/Jun/23 $$\mathrm{25} \\ $$ Answered by MM42 last updated on…
Question Number 193951 by Erico last updated on 23/Jun/23 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}!}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} {t}^{{n}} {e}^{−{t}} {dt}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by senestro last updated on…
Question Number 193235 by mathlove last updated on 08/Jun/23 Answered by a.lgnaoui last updated on 08/Jun/23 $$\boldsymbol{\mathrm{T}}\mathrm{otale}\:\mathrm{Area}=\mathrm{22}+\mathrm{A}\:\:\:\:\:\:\left(\mathrm{A}=\boldsymbol{\mathrm{xy}}\right) \\ $$$$\mathrm{22}+\boldsymbol{\mathrm{xy}}=\mathrm{6}\boldsymbol{\mathrm{x}}+\left(\mathrm{8}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{xy}}=\mathrm{8}\boldsymbol{\mathrm{y}}+\mathrm{6}\boldsymbol{\mathrm{x}}−\mathrm{22} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{xy}}=\mathrm{4}\boldsymbol{\mathrm{y}}+\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{11}\:\:\:\left(\mathrm{1}\right)…