Question Number 131196 by john_santu last updated on 02/Feb/21 $$\:{The}\:{minimum}\:{value}\:{of}\:{the}\: \\ $$$${expression}\:{B}\:=\:\mid{z}\mid^{\mathrm{2}} +\mid{z}−\mathrm{3}\mid^{\mathrm{2}} +\mid{z}−\mathrm{6}{i}\mid^{\mathrm{2}} \\ $$$${is}\:{p}.\:{What}\:{the}\:{value}\:{of}\:\frac{{p}}{\mathrm{10}}\:.? \\ $$ Answered by liberty last updated on 02/Feb/21…
Question Number 12861 by Gauri last updated on 04/May/17 $${change}\mathrm{0}.\mathrm{35}\overset{−} {\mathrm{6}}\:{into}\:{p}/{q}\:{form} \\ $$$$ \\ $$ Answered by mrW1 last updated on 04/May/17 $${x}=\mathrm{0}.\mathrm{35}\bar {\mathrm{6}}=\mathrm{0}.\mathrm{356666666}…… \\…
Question Number 12843 by tawa last updated on 04/May/17 $$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1}.\:\mathrm{and}\:\mathrm{a},\mathrm{b}\:\:\mathrm{member}\:\mathrm{of}\:\mathrm{R}.\:\mathrm{Suppose}\:\mathrm{a}\:\mathrm{is} \\ $$$$\mathrm{invertible}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:+\:\mathrm{b}\:\mathrm{is}\:\mathrm{invertible}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12794 by tawa last updated on 01/May/17 $$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1},\:\mathrm{and}\:\:\mathrm{a},\mathrm{b}\in\mathrm{R}.\:\mathrm{suppose}\:\mathrm{a}\:\mathrm{is}\:\mathrm{ivertible}\:\mathrm{and} \\ $$$$\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{a}\:+\:\mathrm{b}\:\:\mathrm{is}\:\mathrm{ivertible}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143790 by Dwaipayan Shikari last updated on 18/Jun/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{{x}^{\mathrm{3}} }{{n}^{\mathrm{3}} }\right) \\ $$ Commented by Dwaipayan Shikari last updated on 18/Jun/21…
Question Number 12330 by malwaan last updated on 22/Apr/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{fifth}\:\mathrm{digit}\:\mathrm{from}\:\mathrm{the}\:\mathrm{end} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{5}^{\mathrm{5}^{\mathrm{5}^{\mathrm{4}^{\mathrm{5}} } } } \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 12209 by tawa last updated on 16/Apr/17 $$\mathrm{For}\:\mathrm{all}\:\mathrm{n}\:\geqslant\:\mathrm{1}\:,\:\:\mathrm{n}\:\in\:\mathrm{Z},\:\:\mathrm{prove}\:\mathrm{that},\: \\ $$$$\mathrm{p}\left(\mathrm{n}\right)\::\:\mathrm{4}\:+\:\mathrm{8}\:+\:…\:+\:\mathrm{4n}\:=\:\mathrm{2n}\left(\mathrm{n}\:+\:\mathrm{1}\right) \\ $$ Commented by tawa last updated on 16/Apr/17 $$\mathrm{please}\:\mathrm{show}\:\mathrm{me}\:\mathrm{full}\:\mathrm{workings}\:\mathrm{sirs}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{all}. \\ $$ Answered…
Question Number 12106 by tawa last updated on 13/Apr/17 Answered by FilupS last updated on 13/Apr/17 $$\Sigma{a}_{{n}} \:\mathrm{diverges}\:\mathrm{if}:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} \neq\mathrm{0} \\ $$$$\Sigma{ca}_{{n}} ={c}\Sigma{a}_{{n}} \\ $$$$\therefore{c}\Sigma{a}_{{n}}…
Question Number 143085 by Dwaipayan Shikari last updated on 09/Jun/21 $$\phi\left({n}^{\mathrm{4}} +\mathrm{1}\right)=\mathrm{8}{n}\:\:\:\:\:\:\phi:{Euler}\:{totient}\:{function} \\ $$$${Solve}\:{for}\:{n}\in\mathbb{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 11854 by tawa last updated on 02/Apr/17 $$\mathrm{Solve}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:+\:\mathrm{n}}\:=\:\frac{\mathrm{2n}}{\mathrm{n}\:+\:\mathrm{1}} \\ $$ Answered by sandy_suhendra last updated on 03/Apr/17 $$\mathrm{for}\:\mathrm{n}=\mathrm{1} \\ $$$$\mathrm{1}=\frac{\mathrm{2}.\mathrm{1}}{\mathrm{1}+\mathrm{1}}\:\left(\mathrm{is}\:\mathrm{true}\right) \\…