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Author: Tinku Tara

lim-n-1-2-4-1-5-7-1-3n-1-3n-1-

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) \\…

a-b-c-R-S-9a-b-c-16b-a-c-49c-a-b-min-S-

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} \\…

If-x-y-z-xyz-Find-x-1-y-2-1-z-2-y-1-x-2-1-z-2-z-1-x-2-1-y-2-2xyz-

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-214483

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}…

a-b-c-d-e-f-Q-1-2-2-1-3-2-a-2-b-2-c-2-d-2-e-2-f-find-a-b-c-d-e-f-

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…