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Category: Algebra

Let-a-b-0-1-and-a-b-1-Prove-that-1-1-a-1-1-b-1-2-2-a-b-

Question Number 143122 by loveineq last updated on 10/Jun/21 $$\mathrm{Let}\:{a},{b}\:\in\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{and}\:{a}+{b}\:\leqslant\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}+{a}}+\frac{\mathrm{1}}{\mathrm{1}+{b}}+\frac{\mathrm{1}}{\mathrm{2}}\:\leqslant\:\frac{\mathrm{2}}{{a}+{b}}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

cos-3x-sin-2x-0-

Question Number 143105 by mathdanisur last updated on 10/Jun/21 $$\frac{{cos}\left(\mathrm{3}{x}\right)}{{sin}\left(\mathrm{2}{x}\right)}\:=\:\mathrm{0} \\ $$ Commented by Dwaipayan Shikari last updated on 10/Jun/21 $${cos}\left(\mathrm{3}{x}\right)=\mathrm{0}\:\:\: \\ $$$$\mathrm{3}{x}=\left(\mathrm{2}{k}+\mathrm{1}\right)\frac{\pi}{\mathrm{2}}\Rightarrow{x}=\left(\mathrm{2}{k}+\mathrm{1}\right)\frac{\pi}{\mathrm{6}}\:\:\:\:{k}\in\mathbb{Z} \\ $$$${sin}\left(\mathrm{2}{x}\right)\neq\mathrm{0}…

Question-12030

Question Number 12030 by tawa last updated on 09/Apr/17 Answered by mrW1 last updated on 10/Apr/17 $${I}\:{think}\:{none}\:{of}\:{the}\:{answers}\:{is}\:{correct}. \\ $$$${A}.\:{Y}=\mathrm{4} \\ $$$$\mathrm{2}_{\mathrm{9}} ×\left(\mathrm{34}\right)_{\mathrm{9}} =\mathrm{2}×\mathrm{31}=\mathrm{62} \\ $$$$\mathrm{3}_{\mathrm{5}}…

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

Question Number 77556 by behi83417@gmail.com last updated on 07/Jan/20 $$\mathrm{1}.\:\:\:\mathrm{1}×\mathrm{1}!×\mathrm{2}!+\mathrm{2}×\mathrm{2}!×\mathrm{3}!+\mathrm{3}×\mathrm{3}!×\mathrm{4}!+….=? \\ $$$$\mathrm{2}.\:\:\:\:\frac{\mathrm{1}+\sqrt{\mathrm{2}}}{\mathrm{2}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}+\sqrt{\mathrm{3}}}{\mathrm{3}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}+\sqrt{\mathrm{4}}}{\mathrm{4}+\sqrt{\mathrm{5}}}+……=? \\ $$$$\mathrm{3}.\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+\frac{\mathrm{2}}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}}+\frac{\mathrm{3}}{\:\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{5}}}+….=?\: \\ $$ Commented by mr W last updated on 07/Jan/20 $$\mathrm{1}.\:\:\rightarrow\infty,\:{clear}…

Question-77513

Question Number 77513 by BK last updated on 07/Jan/20 Commented by Kunal12588 last updated on 07/Jan/20 -99631646050232081463391082912554874214147786127212261300098296284926069581800964669753771227589064527729684298473399551387739150433334227370085293404740389579109830756667470298828368996394719909762120 Commented by MJS last updated on 07/Jan/20 $$\mathrm{let}'\mathrm{s}\:\mathrm{just}\:\mathrm{give}\:\mathrm{it}\:\mathrm{a}\:\mathrm{name}…