Question Number 194166 by cortano12 last updated on 29/Jun/23 Answered by horsebrand11 last updated on 30/Jun/23 $$\left.\:\:\mathrm{D}\right)\:\mathrm{x}^{\mathrm{3}} +\mathrm{x}\: \\ $$ Terms of Service Privacy Policy…
Question Number 194163 by York12 last updated on 29/Jun/23 $$\boldsymbol{{Let}}\:\boldsymbol{{a}}\:,\:\boldsymbol{{b}}\:,\:\boldsymbol{{c}}\:\:\:\boldsymbol{{be}}\:\boldsymbol{{positive}}\:\boldsymbol{{real}}\:\boldsymbol{{numbers}} \\ $$$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\frac{\boldsymbol{{a}}}{\boldsymbol{{b}}}+\frac{\boldsymbol{{b}}}{\boldsymbol{{c}}}+\frac{\boldsymbol{{c}}}{\boldsymbol{{a}}}+\frac{\mathrm{3}^{\mathrm{3}} \sqrt{{abc}}}{\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}}\geqslant\mathrm{4} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 194159 by Frix last updated on 28/Jun/23 $$…\mathrm{anybody}\:\mathrm{tried}\:\mathrm{question}\:\mathrm{193484}? \\ $$$$\mathrm{It}'\mathrm{s}\:\mathrm{not}\:\mathrm{as}\:\mathrm{hard}\:\mathrm{as}\:\mathrm{it}\:\mathrm{may}\:\mathrm{seem}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 194158 by Frix last updated on 28/Jun/23 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}: \\ $$$$\frac{\mathrm{1}}{{s}}+\frac{\mathrm{1}}{{t}}+\frac{\mathrm{1}}{{u}}+\frac{\mathrm{1}}{{v}}=\mathrm{1} \\ $$$$\mathrm{With}\:{s},\:{t},\:{u},\:{v}\:\in\mathbb{N}\:\mathrm{and}\:{s}<{t}<{u}<{v} \\ $$ Answered by AST last updated on 29/Jun/23 $${s}<{t}\Rightarrow\frac{\mathrm{1}}{{s}}>\frac{\mathrm{1}}{{t}}\Rightarrow\frac{\mathrm{4}}{{s}}>\frac{\mathrm{1}}{{s}}+\frac{\mathrm{1}}{{t}}+\frac{\mathrm{1}}{{u}}+\frac{\mathrm{1}}{{v}}=\mathrm{1}\Rightarrow{s}<\mathrm{4} \\…
Question Number 194144 by mr W last updated on 28/Jun/23 $${fill}\:{with}\:{different}\:{natural}\:{numbers}: \\ $$$$\:\:\frac{\mathrm{1}}{\mathrm{19}}=\frac{\mathrm{1}}{\left(\:\:\right)}+\frac{\mathrm{1}}{\left(\:\:\right)}+\frac{\mathrm{1}}{\left(\:\:\right)}+\frac{\mathrm{1}}{\left(\:\:\right)} \\ $$ Answered by York12 last updated on 28/Jun/23 $${egyptian}\:{fractions} \\ $$$$\frac{\mathrm{1}}{{k}}=\frac{\mathrm{1}}{{k}+\mathrm{1}}+\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}…
Question Number 194147 by DAVONG last updated on 28/Jun/23 $$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+…+\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\right)=? \\ $$ Answered by Frix last updated on 28/Jun/23 $$\frac{\pi^{\mathrm{2}}…
Question Number 194140 by MM42 last updated on 28/Jun/23 $${prove}\:{it}\:: \\ $$$$\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}^{\:\mathrm{2}} \geqslant\:\begin{pmatrix}{\:\:\:\:{n}}\\{{k}−\mathrm{1}}\end{pmatrix}\:×\begin{pmatrix}{\:\:{n}}\\{{k}+\mathrm{1}}\end{pmatrix}\:\:\:\:\:;\:\:\:\mathrm{1}\leqslant{k}\leqslant{n}−\mathrm{1} \\ $$$$ \\ $$ Answered by witcher3 last updated on 28/Jun/23 $$\left(\frac{\mathrm{n}!}{\mathrm{k}!.\left(\mathrm{n}−\mathrm{k}\right)!}\right)^{\mathrm{2}}…
Question Number 194143 by mathbd last updated on 28/Jun/23 Commented by a.lgnaoui last updated on 29/Jun/23 $$\mathrm{H}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 194139 by cortano12 last updated on 28/Jun/23 Commented by MM42 last updated on 28/Jun/23 $${for} \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{x}^{\mathrm{2}} +\mathrm{2}{cosx}−\mathrm{2}}{{x}^{\mathrm{4}} }\:\rightarrow{hop} \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{2}\left({x}−{sinx}\right)}{\mathrm{4}{x}^{\mathrm{3}}…
Question Number 194135 by cortano12 last updated on 28/Jun/23 $$\:\:\:\:\:\:\begin{array}{|c|}{\frac{\mathrm{23}!−\mathrm{23}}{\mathrm{1}.\mathrm{1}!+\mathrm{2}.\mathrm{2}!+\mathrm{3}.\mathrm{3}!+…+\mathrm{21}.\mathrm{21}!}\:=?}\\\hline\end{array} \\ $$ Answered by Frix last updated on 28/Jun/23 $$\mathrm{23} \\ $$$$\left[\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}{j}×{j}!=\left({n}+\mathrm{1}\right)!−\mathrm{1}\right] \\…