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Author: Tinku Tara

how-to-prove-that-the-number-is-divisible-by-3-then-the-number-of-numbers-is-a-multiple-of-3-

Question Number 81647 by john santu last updated on 14/Feb/20 $$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3} \\ $$ Commented by mr W last updated on 14/Feb/20…

let-a-1-gt-a-2-gt-0-and-a-n-1-a-n-a-n-1-where-n-is-greater-than-equal-to-2-Then-The-sequence-a-2n-is-1-monotonic-increasing-2-monotonic-decreasing-3-non-monotonic-4-unbound

Question Number 16110 by vpawarksp@gmail.com last updated on 18/Jun/17 $$\mathrm{let}\:\mathrm{a}_{\mathrm{1}} >\mathrm{a}_{\mathrm{2}} >\mathrm{0}\:\mathrm{and}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} =\sqrt{\mathrm{a}_{\mathrm{n}} \mathrm{a}_{\mathrm{n}−\mathrm{1}\:\:\:} } \\ $$$$\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{2}\: \\ $$$$\mathrm{Then} \\ $$$$\mathrm{The}\:\mathrm{sequence}\:\left\{\mathrm{a}_{\mathrm{2n}} \right\}\:\mathrm{is}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{monotonic}\:\mathrm{increasing} \\…

prove-that-e-2-3-gt-13-2-6-2-

Question Number 147183 by mathdanisur last updated on 18/Jul/21 $${prove}\:{that} \\ $$$$\boldsymbol{{e}}^{\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}} \:>\:\frac{\mathrm{13}\:+\:\mathrm{2}\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$ Answered by mindispower last updated on 18/Jul/21 $$\Leftrightarrow{e}^{\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}} >\mathrm{1}+\mathrm{3}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)\left({E}\right) \\…