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Question-68952

Question Number 68952 by aliesam last updated on 17/Sep/19 Answered by mind is power last updated on 17/Sep/19 $$\Rightarrow{x}−\mathrm{1}>\mathrm{0}\Rightarrow{x}>\mathrm{1} \\ $$$$\Leftrightarrow\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\leqslant\frac{{x}+\mathrm{1}+\mathrm{3}}{{x}−\mathrm{1}}\Rightarrow\left({x}−\mathrm{1}\right)^{\mathrm{2}} \leqslant\left({x}+\mathrm{4}\right)\left({x}+\mathrm{1}\right) \\ $$$$\Leftrightarrow{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}\leqslant{x}^{\mathrm{2}}…

Question-134484

Question Number 134484 by mohammad17 last updated on 04/Mar/21 Commented by Dwaipayan Shikari last updated on 04/Mar/21 $${General}\:{term}=\frac{{n}}{{n}^{\mathrm{2}} −\left({n}−\mathrm{1}\right)^{\mathrm{2}} }=\frac{{n}}{\mathrm{2}{n}−\mathrm{1}} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}}{\mathrm{2}{n}−\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\left({Sequence}\:{converges}\:{to}\:\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$${And}\:{the}\:{series}\:{is}\:{Divergent}\:\underset{{n}=\mathrm{1}}…

Question-68946

Question Number 68946 by ramirez105 last updated on 17/Sep/19 Commented by kaivan.ahmadi last updated on 17/Sep/19 $$\frac{\partial{u}}{\partial{x}}=\left(\mathrm{2}{xy}−{tany}\right)\Rightarrow{u}\left({x},{y}\right)={x}^{\mathrm{2}} {y}−{xtany}+{h}\left({y}\right) \\ $$$$\frac{\partial{u}}{\partial{y}}={x}^{\mathrm{2}} −{xsec}^{\mathrm{2}} {y}={x}^{\mathrm{2}} −{xsec}^{\mathrm{2}} {y}+\frac{{dh}}{{dy}}\Rightarrow\frac{{dh}}{{dy}}=\mathrm{0}\Rightarrow{h}={c}' \\…

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Question Number 3411 by Filup last updated on 13/Dec/15 $$\mathrm{Can}\:\mathrm{someone}\:\mathrm{show}\:\mathrm{me}\:\mathrm{how}: \\ $$$$\left({i}\right)\:\:\:\:\left({x}+{a}\right)^{{v}} =\underset{{k}=\mathrm{0}} {\overset{{v}} {\sum}}\begin{pmatrix}{{v}}\\{{k}}\end{pmatrix}\:{x}^{{v}−{k}} {a}^{{k}} \\ $$$$\left({ii}\right)\:\:\mathrm{Does}: \\ $$$$\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{v}} {\sum}}\begin{pmatrix}{{v}}\\{{k}}\end{pmatrix}\:{x}^{{v}−{k}} {a}^{{k}} =\underset{{k}=\mathrm{0}} {\overset{{v}}…

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Question Number 68947 by Cmr 237 last updated on 20/Oct/19 $$\mathrm{please} \\ $$$$\mathrm{utilise}\:\mathrm{cette}\:\mathrm{fonction}\:\mathrm{to}\: \\ $$$$\mathrm{sh}\boldsymbol{\mathrm{ow}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{N}}\ast\boldsymbol{\mathrm{N}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{denombrable}} \\ $$$$\:\mathrm{f}:\boldsymbol{\mathrm{N}}\circledast\boldsymbol{\mathrm{N}}\rightarrow\boldsymbol{\mathrm{N}} \\ $$$$\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)\shortmid\rightarrow\frac{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{y}+\mathrm{1}\right)}{\mathrm{2}}+\mathrm{y} \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{f}\:\mathrm{est}\:\mathrm{bijective} \\ $$$$\:\:\:\boldsymbol{\mathrm{P}}\mathrm{lease}\:\mathrm{help} \\ $$$$…

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Question Number 3410 by 123456 last updated on 13/Dec/15 $$\mathrm{lets}\:\left({u},{v},{w}\right)\in\mathbb{C}^{\mathrm{3}} \:\mathrm{such}\:\mathrm{that}\:{uvw}\neq\mathrm{0},\:\mathrm{proof} \\ $$$$\mathrm{that}\:\left(\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\right) \\ $$$$\frac{{v}}{{u}}=\frac{{w}}{{v}}\wedge\mid{u}\mid=\mid{v}\mid=\mid{w}\mid\wedge{u}\neq{w}\Rightarrow{u}+{v}+{w}=\mathrm{0} \\ $$ Commented by RasheedSindhi last updated on 13/Dec/15 $$\mathcal{W}{hat}\:{is}\:{meant}\:{by}\:{u},{v},{w}\in\mathbb{C}^{\mathrm{3}}…