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Category: Arithmetic

1-2-2-3-3-4-4-5-

Question Number 176054 by BaliramKumar last updated on 11/Sep/22 $$\frac{\mathrm{1}}{\mathrm{2}!}\:+\:\frac{\mathrm{2}}{\mathrm{3}!}\:+\:\frac{\mathrm{3}}{\mathrm{4}!}\:+\:\frac{\mathrm{4}}{\mathrm{5}!}\:+\:………….\:\infty\:=\:? \\ $$ Answered by Ar Brandon last updated on 11/Sep/22 $${S}=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{{n}−\mathrm{1}}{{n}!}=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)!}−\underset{{n}=\mathrm{2}}…

Question-175758

Question Number 175758 by Stephan last updated on 06/Sep/22 Answered by Jamshidbek last updated on 06/Sep/22 $$\mathrm{Solution}. \\ $$$$\mathrm{we}\:\mathrm{know}\:\mathrm{tr}\left(\mathrm{XY}\right)=\mathrm{tr}\left(\mathrm{YX}\right)\:\Rightarrow\:\mathrm{tr}\left(\mathrm{XY}\right)=\mathrm{1} \\ $$$$\mathrm{U}+\mathrm{V}=\mathrm{1}\:\left[\mathrm{1}\right] \\ $$$$\mathrm{det}\left(\mathrm{XY}\right)=\mathrm{det}\left(\mathrm{X}\right)\mathrm{det}\left(\mathrm{Y}\right) \\ $$$$\mathrm{det}\left(\mathrm{YX}\right)=\mathrm{det}\left(\mathrm{X}\right)\mathrm{det}\left(\mathrm{Y}\right)…

Given-the-equation-of-two-circles-C-1-x-2-y-2-6x-4y-9-0-andC-2-x-2-y-2-2x-6y-9-0-find-the-equation-of-the-common-tangent-to-both-circles-

Question Number 110181 by Rio Michael last updated on 27/Aug/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{two}\:\mathrm{circles} \\ $$$${C}_{\mathrm{1}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\mathrm{6}{x}−\mathrm{4}{y}\:+\:\mathrm{9}\:=\:\mathrm{0}\:\mathrm{and}{C}_{\mathrm{2}} \::\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{6}{y}\:+\:\mathrm{9}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{both}\:\mathrm{circles}. \\ $$ Commented by…

Question-109950

Question Number 109950 by 675480065 last updated on 26/Aug/20 Answered by Aziztisffola last updated on 26/Aug/20 $$\:\left(\mathrm{i}\right)\:\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} >\mathrm{0}\:\Rightarrow\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{1}>\mathrm{0} \\ $$$$\:\Rightarrow\mathrm{x}^{\mathrm{2}} >\mathrm{2x}−\mathrm{1}\:\underset{\mathrm{2x}−\mathrm{1}>\mathrm{1}} {\overset{\mathrm{x}>\mathrm{1}} {\Rightarrow}}\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2x}−\mathrm{1}}>\mathrm{1}…