Question Number 92820 by prince 5 last updated on 13/May/20 $${a}\:{convergent}\:{geometric}\:{sequence}\:{with} \\ $$$${first}\:{term}\:{a}\:{is}\:{such}\:{that}\:{the}\:{sum}\:{of} \\ $$$${the}\:{terms}\:{after}\:{the}\:{n}^{{th}} \:{term}\:{is} \\ $$$${three}\:{times}\:{the}\:{n}^{{th}} \:{term},\:{find}\:{the} \\ $$$${common}\:{ratio}\:{and}\:{show}\:{that}\:{its}\: \\ $$$${sum}\:{to}\:{infinity}\:{is}\:\mathrm{4}{a}. \\ $$…
Question Number 158331 by HongKing last updated on 02/Nov/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}}\:\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:<\:\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92778 by unknown last updated on 09/May/20 Commented by prakash jain last updated on 09/May/20 $$\lfloor\mathrm{3}{x}\rfloor−\mathrm{2}−\left(\lfloor\mathrm{2}{x}\rfloor−\mathrm{1}\right)=\mathrm{2}{x}−\mathrm{6} \\ $$$$\lfloor\mathrm{3}{x}\rfloor−\lfloor\mathrm{2}{x}\rfloor=\mathrm{2}{x}−\mathrm{5}\: \\ $$$$\mathrm{since}\:\mathrm{LHS}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{RHS} \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{integer} \\…
Question Number 158313 by mnjuly1970 last updated on 02/Nov/21 Answered by mr W last updated on 02/Nov/21 $$\alpha,\beta,\gamma\:{are}\:{angles}\:{of}\:{a}\:{triangle}. \\ $$$${F}=\frac{\mathrm{sin}\:\alpha\:\mathrm{cos}\:\alpha+\mathrm{sin}\:\beta\:\mathrm{cos}\:\beta+\mathrm{sin}\:\gamma\:\mathrm{cos}\:\gamma}{\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\ $$$${F}=\frac{\mathrm{sin}\:\mathrm{2}\alpha+\mathrm{sin}\:\mathrm{2}\beta+\mathrm{sin}\:\mathrm{2}\gamma}{\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\ $$$${F}=\frac{\mathrm{4}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma}{\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \\…
Question Number 158303 by HongKing last updated on 02/Nov/21 $$\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}>\mathrm{0} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{8x}^{\mathrm{4}} \:+\:\mathrm{64y}^{\mathrm{4}} \:+\:\mathrm{216z}^{\mathrm{4}} \:+\:\mathrm{1728t}^{\mathrm{4}} \:=\:\mathrm{1}}\\{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:+\:\mathrm{t}\:=\:\mathrm{1}}\end{cases} \\ $$$$ \\ $$ Answered by mr…
Question Number 158295 by HongKing last updated on 02/Nov/21 $$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{sin}^{-\mathrm{1}} \:\mathrm{x}\:\mathrm{log}\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 27213 by shiv15031973@gmail.com last updated on 04/Jan/18 $$\left[\left(\mathrm{16}{x}^{\mathrm{4}} −\mathrm{1}\right)\right]/\left[\mathrm{2}{x}−\mathrm{1}\right]\:{factorise}\:{it} \\ $$ Commented by abdo imad last updated on 03/Jan/18 $$\mathrm{16}\:{x}^{\mathrm{4}} \:−\mathrm{1}\:=\:\:\left(\mathrm{4}{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:−\mathrm{1}\:=\:\left(\mathrm{4}{x}^{\mathrm{2}}…
Question Number 158276 by HongKing last updated on 01/Nov/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{then}: \\ $$$$\mathrm{2}\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\:\geqslant\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \right)\:+\:\mathrm{xyz}\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right) \\ $$$$ \\ $$ Terms of…
Question Number 158281 by Ari last updated on 01/Nov/21 Commented by Ari last updated on 01/Nov/21 Find the constant term on the decomposition of expression Commented by cortano last updated on 02/Nov/21 $$\Rightarrow\left(\mathrm{2}+\mathrm{3}{x}\right)^{\mathrm{3}}…
Question Number 158273 by HongKing last updated on 01/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com