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Question Number 208121 by mokys last updated on 05/Jun/24 Commented by mokys last updated on 06/Jun/24 $$????? \\ $$ Commented by Frix last updated on…
Question Number 208105 by hardmath last updated on 05/Jun/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{8}}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{64}}\:\:+\:\:\frac{\mathrm{4}}{\mathrm{256}}\:\:+\:\:…\:\:+\:\:=\:\:? \\ $$ Commented by Frix last updated on 05/Jun/24 $$=\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{2}}{\mathrm{16}}+\frac{\mathrm{3}}{\mathrm{64}}+\frac{\mathrm{4}}{\mathrm{256}}+…= \\ $$$$=\underset{{k}=\mathrm{1}} {\overset{\infty}…
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Question Number 208106 by Ismoiljon_008 last updated on 05/Jun/24 Answered by cherokeesay last updated on 05/Jun/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 208103 by depressiveshrek last updated on 05/Jun/24 $$\mathrm{Find}\:\mathrm{inf}\left\{\frac{{m}}{{n}}\:\mid\:{m},\:{n}\:\in\:\mathbb{N},\:{m}<{n}−\mathrm{2}\right\} \\ $$ Answered by A5T last updated on 05/Jun/24 $${Since}\:{m},{n}\in\mathbb{N},\:\frac{{m}}{{n}}>\mathrm{0},{so}\:\mathrm{0}\:{is}\:{a}\:{lower}\:{bound}. \\ $$$$\frac{{m}}{{n}}\geqslant\frac{\mathrm{1}}{{n}}\:{and}\:\frac{\mathrm{1}}{{n}}\:{is}\:{in}\:{the}\:{set}. \\ $$$${For}\:{any}\:\epsilon>\mathrm{0},\:{one}\:{can}\:{always}\:{find}\:{n}\:{such}\:{that} \\…
Question Number 208097 by efronzo1 last updated on 05/Jun/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by MM42 last updated on 05/Jun/24 $$\mathrm{2}^{{x}−{m}+\mathrm{1}} −\mathrm{2}^{{x}−{m}} \:=\mathrm{8} \\ $$$$\Rightarrow\mathrm{2}^{{x}−{m}} =\mathrm{8}\Rightarrow{x}−{m}=\mathrm{3}\Rightarrow{x}={m}+\mathrm{3}…
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Question Number 208076 by hardmath last updated on 04/Jun/24 $$\left(\mathrm{5}\:−\:\mid\mathrm{x}\mid\right)^{−\:\frac{\mathrm{1}}{\mathrm{3}}} \:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right)\:<\:\mathrm{0} \\ $$ Answered by TonyCWX08 last updated on 04/Jun/24 $${This}\:{inequality}\:{are}\:{defined}\:{when}\:{x}\in\langle−\mathrm{5},\mathrm{5}\rangle \\ $$$${Two}\:{Possible}\:{Cases} \\…