Question Number 128290 by mr W last updated on 06/Jan/21 $${find}\:\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−……}}}}=? \\ $$$$\left({A}\right)\:\:\:\:\:\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}} \\ $$$$\left({B}\right)\:\:\:\:\:\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}} \\ $$$$\left({C}\right)\:\:\:\:\:\mathrm{5}\pm\mathrm{2}\sqrt{\mathrm{6}} \\ $$$$\left({D}\right)\:\:\:\:\:{none}\:{of}\:{above} \\ $$$$ \\ $$$${please}\:{give}\:{your}\:{answer}\:{and}\:{explain} \\ $$$${why}!…
Question Number 128264 by bobhans last updated on 06/Jan/21 $$\sqrt[{\mathrm{8}\:\:\:\:}]{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−…}}}}} \\ $$ Commented by MJS_new last updated on 06/Jan/21 $$\frac{\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Commented by bobhans…
Question Number 128232 by math35 last updated on 05/Jan/21 $$\mathrm{1}.\mathrm{For}\:\mathrm{n}\in\mathbb{N},\mathrm{define}\:\:\mathrm{s}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}^{\mathrm{2}^{\mathrm{n}} } +\mathrm{2}^{\mathrm{2}^{\mathrm{n}+\mathrm{1}} } .\mathrm{Which}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{false}\:\mathrm{for}\:\mathrm{some}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\in\mathbb{N}? \\ $$$$\mathrm{A}.\mathrm{3}\mid\mathrm{s}_{\mathrm{n}} \\ $$$$\mathrm{B}.\mathrm{7}\mid\mathrm{s}_{\mathrm{n}} \\ $$$$\mathrm{C}.\mathrm{s}_{\mathrm{n}} \mid\mathrm{s}_{\mathrm{n}+\mathrm{1}} \\…
Question Number 62672 by bshahid010@gmail.com last updated on 24/Jun/19 Commented by Rasheed.Sindhi last updated on 24/Jun/19 $$\mathrm{b}\in\mathrm{I},\:\mathrm{I}\:{means}\:{irrational}? \\ $$ Commented by mr W last updated…
Question Number 62676 by bshahid010@gmail.com last updated on 24/Jun/19 Commented by kaivan.ahmadi last updated on 24/Jun/19 $${if}\:{tanx}={n}>\mathrm{0}\Rightarrow \\ $$$${n}^{\mathrm{2}} +{an}+{n}+{a}−\mathrm{3}<\mathrm{0}\Rightarrow{a}\left({n}+\mathrm{1}\right)<\mathrm{3}−{n}^{\mathrm{2}} −{n}\Rightarrow \\ $$$${a}<\frac{\mathrm{3}−{n}−{n}^{\mathrm{2}} }{{n}+\mathrm{1}} \\…
Question Number 128204 by I want to learn more last updated on 05/Jan/21 $$\mathrm{Let}\:\:\:\mathrm{x},\:\:\mathrm{y},\:\:\mathrm{z}\:\:\:\mathrm{be}\:\mathrm{pairwise}\:\mathrm{distinct}\:\mathrm{real}\:\mathrm{numbers},\:\mathrm{if} \\ $$$$\:\:\left(\mathrm{x}\:\:+\:\:\mathrm{y}\:\:−\:\:\mathrm{7}\right)\left[\mathrm{z}\left(\mathrm{x}\:\:+\:\:\mathrm{y}\right)\:\:+\:\:\mathrm{24}\right]\:\:\:=\:\:\left(\mathrm{y}\:\:+\:\:\mathrm{z}\:\:−\:\:\mathrm{7}\right)\left[\mathrm{x}\left(\mathrm{y}\:\:+\:\:\mathrm{z}\right)\:\:+\:\:\mathrm{24}\right]\:\:\:=\:\:\:\left(\mathrm{z}\:\:+\:\:\mathrm{x}\:\:−\:\:\mathrm{7}\right)\left[\mathrm{y}\left(\mathrm{z}\:\:+\:\:\mathrm{x}\right)\:\:+\:\:\mathrm{24}\right] \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{y}^{\mathrm{2}} \:\:+\:\:\mathrm{z}^{\mathrm{2}} \\ $$ Terms of Service…
Question Number 62669 by Sayantan chakraborty last updated on 24/Jun/19 $${calculate}\:{the}\:{value}\:{of}\:\underset{{n}=\mathrm{0}} {\overset{\mathrm{1947}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{{n}} +\sqrt{\mathrm{2}^{\mathrm{1947}} }} \\ $$ Answered by tanmay last updated on 24/Jun/19 $${a}=\sqrt{\mathrm{2}^{\mathrm{1947}}…
Question Number 128166 by bramlexs22 last updated on 05/Jan/21 $$\:\sqrt{\mathrm{x}−\mathrm{2}}\:+\:\sqrt{\mathrm{x}+\mathrm{3}}\:+\sqrt{\mathrm{4x}+\mathrm{1}}\:=\:\mathrm{10} \\ $$$$\:\mathrm{for}\:\mathrm{x}\in\mathbb{R}\: \\ $$ Answered by liberty last updated on 05/Jan/21 $$\:\sqrt{\mathrm{4x}+\mathrm{1}}\:=\:\left[\:−\sqrt{\mathrm{x}+\mathrm{3}}−\sqrt{\mathrm{x}−\mathrm{2}}+\mathrm{10}\:\right] \\ $$$$\:\mathrm{4x}+\mathrm{1}\:=\:\mathrm{2}\sqrt{\mathrm{x}−\mathrm{2}\:}\:\sqrt{\mathrm{x}+\mathrm{3}}\:−\mathrm{20}\sqrt{\mathrm{x}+\mathrm{3}}\:+\mathrm{2x}\:−\mathrm{20}\sqrt{\mathrm{x}−\mathrm{2}}\:+\mathrm{101} \\…
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