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Category: Algebra

Question-172448

Question Number 172448 by Shrinava last updated on 27/Jun/22 Answered by Jamshidbek last updated on 28/Jun/22 $$\mathrm{Let}\:\:\frac{\mathrm{1}!!}{\mathrm{0}!}+\frac{\mathrm{3}!!}{\mathrm{1}!}+\frac{\mathrm{5}!!}{\mathrm{2}!}+…+\frac{\left(\mathrm{2n}+\mathrm{1}\right)!!}{\mathrm{n}!}=\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{and}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} −\mathrm{a}_{\mathrm{n}} =\frac{\left(\mathrm{2n}+\mathrm{3}\right)!!}{\left(\mathrm{n}+\mathrm{1}\right)!} \\ $$$$\Omega=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{a}_{\mathrm{n}}…

Question-106907

Question Number 106907 by Study last updated on 07/Aug/20 Answered by Don08q last updated on 08/Aug/20 $$\:\:\:\:\:\:=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{8}} \left(\mathrm{64}\right)^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{39}} } \right)\:\underset{} {\:} \\ $$$$\:\:\:\:\:\:=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{8}}…

Question-172360

Question Number 172360 by Mikenice last updated on 25/Jun/22 Commented by mr W last updated on 25/Jun/22 $$\left(\mathrm{1}\right) \\ $$$$\mathrm{4}=\sqrt{\mathrm{16}}=\sqrt{\mathrm{13}+\sqrt{\mathrm{9}}}=\sqrt{\mathrm{13}+\sqrt{\mathrm{5}+\mathrm{4}}}=\sqrt{\mathrm{13}+\sqrt{\mathrm{5}+\sqrt{\mathrm{13}+\sqrt{\mathrm{5}+\sqrt{\mathrm{13}+…}}}}} \\ $$ Commented by mr…

prove-by-mathematical-induction-1-n-2-2-n-n-4-2-n-1-2-lt-2n-2-n-3-3-2-n-3-2-n-2-n-5-bemath-

Question Number 106816 by bemath last updated on 07/Aug/20 $$\mathrm{prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{n}^{\mathrm{2}} \:\leqslant\:\mathrm{2}^{\mathrm{n}} \:;\:\mathrm{n}\:\geqslant\:\mathrm{4} \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}} \:<\:\mathrm{2n}^{\mathrm{2}} \:;\:\mathrm{n}\:\geqslant\:\mathrm{3} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{2}^{\mathrm{n}} −\mathrm{3}\:\geqslant\:\mathrm{2}^{\mathrm{n}−\mathrm{2}} \:;\:\mathrm{n}\:\geqslant\:\mathrm{5} \\ $$$$\:\:\:\:\:\:@\mathrm{bemath}@ \\…

repost-old-question-unanswer-Given-4x-2-1-4x-2-y-4y-2-1-4y-2-z-4z-2-1-4z-2-x-

Question Number 106794 by bobhans last updated on 07/Aug/20 $$\mathrm{repost}\:\mathrm{old}\:\mathrm{question}\:\mathrm{unanswer} \\ $$$$\mathcal{G}\mathrm{iven}\:\rightarrow\begin{cases}{\frac{\mathrm{4x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{4x}^{\mathrm{2}} }\:=\:\mathrm{y}}\\{\frac{\mathrm{4y}^{\mathrm{2}} }{\mathrm{1}+\mathrm{4y}^{\mathrm{2}} }\:=\:\mathrm{z}}\\{\frac{\mathrm{4z}^{\mathrm{2}} }{\mathrm{1}+\mathrm{4z}^{\mathrm{2}} }\:=\:\mathrm{x}}\end{cases} \\ $$ Answered by thearith last updated…