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Question-134526

Question Number 134526 by mohammad17 last updated on 04/Mar/21 Answered by mr W last updated on 05/Mar/21 $$\frac{\mathrm{1}}{\mathrm{1}+{x}}=\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +… \\ $$$$\int\frac{\mathrm{1}}{\mathrm{1}+{x}}{dx}=\int\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +…\right){dx} \\…

let-a-b-be-any-two-elements-in-group-G-such-that-a-4-b-2-and-a-3-b-ab-find-ab-help-me-sir-please-

Question Number 134523 by mohammad17 last updated on 04/Mar/21 $${let}\:{a},{b}\:{be}\:{any}\:{two}\:{elements}\:{in}\:{group}\:{G} \\ $$$${such}\:{that}\:\mid{a}\mid=\mathrm{4}\:,\mid{b}\mid=\mathrm{2}\:{and}\:{a}^{\mathrm{3}} {b}={ab} \\ $$$${find}\:\mid{ab}\mid\:? \\ $$$${help}\:{me}\:{sir}\:{please} \\ $$ Commented by kaivan.ahmadi last updated on…

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}}…