Question Number 214485 by depressiveshrek last updated on 09/Dec/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{7}}+…+\frac{\mathrm{1}}{\left(\mathrm{3}{n}−\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{1}\right)}\right) \\ $$ Answered by mr W last updated on 10/Dec/24 $$\psi\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}}\right)=−\gamma+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}−\frac{\mathrm{1}}{\mathrm{3}}}\right) \\…
Question Number 214454 by hardmath last updated on 09/Dec/24 $$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\mathbb{R}^{+} \\ $$$$\mathrm{S}\:\:=\:\:\frac{\mathrm{9a}}{\mathrm{b}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{16b}}{\mathrm{a}\:+\:\mathrm{c}}\:\:+\:\:\frac{\mathrm{49c}}{\mathrm{a}\:+\:\mathrm{b}} \\ $$$$\boldsymbol{\mathrm{min}}\left(\mathrm{S}\right)\:=\:? \\ $$ Commented by Ghisom last updated on 09/Dec/24 $${S}>\mathrm{24} \\…
Question Number 214471 by issac last updated on 09/Dec/24 $${d}^{\mathrm{2}} −{d}+\mathrm{2}=\mathrm{0} \\ $$$$\underset{{k};\:{d}^{\mathrm{2}} −{d}+\mathrm{2}=\mathrm{0}} {\sum}\:\frac{\mathrm{1}}{{k}}=?? \\ $$ Answered by mr W last updated on 09/Dec/24…
Question Number 214455 by hardmath last updated on 09/Dec/24 $$\mathrm{If}\:\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{xyz} \\ $$$$\mathrm{Find}: \\ $$$$\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{y}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{z}^{\mathrm{2}} \right)+\mathrm{z}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{2xyz}} \\ $$ Commented by Ghisom…
Question Number 214483 by MATHEMATICSAM last updated on 09/Dec/24 Answered by ajfour last updated on 09/Dec/24 $${let}\:{C}\equiv\left({h},\:\mathrm{2}−{r}\right) \\ $$$$\left({x}−{h}\right)^{\mathrm{2}} +\left({mx}^{\mathrm{2}} −\mathrm{2}+{r}\right)^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$\frac{{h}−{x}}{{mx}^{\mathrm{2}} −\mathrm{2}+{r}}=\mathrm{2}{mx}…
Question Number 214447 by 2universe456 last updated on 08/Dec/24 Commented by Frix last updated on 08/Dec/24 $$={abc} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 214443 by hardmath last updated on 08/Dec/24 $$\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:\in\:\mathrm{Q} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{2}}}\:=\:\mathrm{2}^{\boldsymbol{\mathrm{a}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{b}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{c}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{d}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{e}}} \:+\:\mathrm{2}^{\boldsymbol{\mathrm{f}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f}\:=\:? \\ $$ Answered by ajfour last…
Question Number 214427 by ajfour last updated on 08/Dec/24 Commented by ajfour last updated on 08/Dec/24 https://youtu.be/pnMSZ77i2P8?si=OaLd0p_DlkwNYv8d Answered by a.lgnaoui last updated on 08/Dec/24 $$\mathrm{Resolution}\:\mathrm{de}\:\mathrm{l}\:\mathrm{equation}\:\mathrm{donne}…
Question Number 214421 by ChantalYah last updated on 08/Dec/24 Answered by TonyCWX08 last updated on 08/Dec/24 $${Use}\:{Newton}'{s}\:{Identity} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 214448 by jahar last updated on 08/Dec/24 $$ \\ $$$$\overset{−} {{x}}\:=\:\frac{\Sigma{f}_{{i}} {x}_{{i}} }{\Sigma{f}_{{i}} \:}\:,\:\:\:\overset{−} {{u}}\:=\:\frac{\Sigma{f}_{{i}} {u}_{{i}} }{\Sigma{f}_{{i}} }\:,\:{u}\:=\:\frac{{x}−{a}}{{h}}\:, \\ $$$${proved}\:{that}\:\overset{−} {{x}}\:=\:{a}\:+\:{h}\overset{−} {{u}} \\…