Question Number 196164 by Rodier97 last updated on 19/Aug/23 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{calcul}: \\ $$$$ \\ $$$$\:\:\:{lim}_{{n}\rightarrow+\infty\:\:\:\:} {Un}=\sqrt[{{n}}]{\frac{\left(\mathrm{2}{n}\right)!}{{n}!{n}^{{n}} }} \\ $$$$ \\ $$$$ \\…
Question Number 196198 by liuxinnan last updated on 19/Aug/23 $${a}+{b}+{c}+{d}=\mathrm{4} \\ $$$${prove}\:{that}: \\ $$$$\frac{{a}}{{a}^{\mathrm{3}} +\mathrm{8}}+\frac{{b}}{{b}^{\mathrm{3}} +\mathrm{8}}+\frac{{c}}{{c}^{\mathrm{3}} +\mathrm{8}}+\frac{{d}}{{d}^{\mathrm{3}} +\mathrm{8}}\leq\frac{\mathrm{4}}{\mathrm{9}} \\ $$ Answered by AST last updated…
Question Number 196094 by leicianocosta last updated on 18/Aug/23 Answered by dimentri last updated on 18/Aug/23 $$\left(\mathrm{1}\right)\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{2}^{\mathrm{3}\left({n}−\mathrm{1}\right)} }{\mathrm{3}^{\mathrm{2}{n}} }\right)=\:\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{8}}{\mathrm{81}}+\frac{\mathrm{64}}{\mathrm{729}}+\ldots \\ $$$$\:\:\:\:\:\:=\:\frac{\frac{\mathrm{1}}{\mathrm{9}}}{\mathrm{1}−\frac{\mathrm{8}}{\mathrm{9}}}\:=\:\mathrm{1}\: \\ $$…
Question Number 196132 by sonukgindia last updated on 18/Aug/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196134 by sonukgindia last updated on 18/Aug/23 Answered by AST last updated on 18/Aug/23 $$\left[{log}\left({x}\right)+{log}\left({y}\right)\right]^{\mathrm{2}} −\mathrm{2}{log}\left({x}\right){log}\left({y}\right)=\mathrm{2}{log}\left({xy}\right) \\ $$$$\Rightarrow\left[{log}\left({xy}\right)\right]^{\mathrm{2}} =\mathrm{2}\left[{log}\left({xy}\right)+{log}\left({x}\right){log}\left({y}\right)\right]…\left({i}\right) \\ $$$${Let}\:\left[{log}\left({xy}\right)\right]={t};\left({i}\right)\Rightarrow{t}^{\mathrm{2}} −\mathrm{2}{t}=\mathrm{2}{log}\left({x}\right){log}\left({y}\right) \\…
Question Number 196117 by sonukgindia last updated on 18/Aug/23 Answered by Rasheed.Sindhi last updated on 18/Aug/23 $${m}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{n}^{\mathrm{2}} \right)−\mathrm{10}\left(\mathrm{3}{n}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{517}−\mathrm{10} \\ $$$$\left({m}^{\mathrm{2}} −\mathrm{10}\right)\left(\mathrm{3}{n}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{507} \\…
Question Number 196115 by sonukgindia last updated on 18/Aug/23 Answered by Rasheed.Sindhi last updated on 18/Aug/23 $${xy}+\mathrm{66}{x}−\mathrm{88}{y}−\mathrm{88}×\mathrm{66}=\mathrm{23333}−\mathrm{88}×\mathrm{66} \\ $$$${x}\left({y}+\mathrm{66}\right)−\mathrm{88}\left({y}+\mathrm{66}\right)=\mathrm{17525} \\ $$$$\left({x}−\mathrm{88}\right)\left({y}+\mathrm{66}\right)=\mathrm{5}^{\mathrm{2}} ×\mathrm{701}\: \\ $$$$\begin{cases}{\underset{{x}=\mathrm{89}\:} {{x}−\mathrm{88}=\mathrm{1}}\:\wedge\:\underset{{y}=\mathrm{23267}}…
Question Number 196111 by sonukgindia last updated on 18/Aug/23 Answered by mahdipoor last updated on 18/Aug/23 $$\Rightarrow\Rightarrow\Rightarrow\Rightarrow\:{if}\:{n}\leqslant{x}\:\Rightarrow \\ $$$$\Sigma=\left({x}−\mathrm{1}\right)+…+\left({x}−{n}\right)={nx}−\frac{{n}^{\mathrm{2}} +{n}}{\mathrm{2}}= \\ $$$${x}^{\mathrm{2}} −\left({n}+\mathrm{1}\right){x}+\left(\frac{{n}^{\mathrm{2}} +\mathrm{2}{n}+\mathrm{5}}{\mathrm{4}}\right) \\…
Question Number 196103 by MrGHK last updated on 18/Aug/23 $$\frac{\boldsymbol{\mathrm{d}}^{\boldsymbol{\mathrm{n}}} }{\boldsymbol{\mathrm{dx}}^{\boldsymbol{\mathrm{n}}} }\left[\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{x}}\right)\right]\:\:\boldsymbol{\mathrm{Hence}}\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\frac{\boldsymbol{\mathrm{d}}^{\frac{\mathrm{1}}{\mathrm{2}}} }{\boldsymbol{\mathrm{dx}}^{\frac{\mathrm{1}}{\mathrm{2}}} }\left[\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{x}}\right)\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196097 by leicianocosta last updated on 18/Aug/23 Terms of Service Privacy Policy Contact: info@tinkutara.com