Question Number 56415 by gunawan last updated on 16/Mar/19 $$\mathrm{If}\:\:\:\mathrm{for}\:\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\:, \\ $$$$\:{y}={exp}\left[\left(\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{4}} {x}+\mathrm{sin}^{\mathrm{6}} {x}+…\infty\right)\mathrm{log}_{{e}} \mathrm{2}\right] \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{zero}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$${x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{8}=\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}\:\mathrm{is} \\ $$ Answered by…
Question Number 56414 by gunawan last updated on 16/Mar/19 $$\mathrm{If}\:\:\:\mathrm{for}\:\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\:, \\ $$$$\:{y}={exp}\left[\left(\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{4}} {x}+\mathrm{sin}^{\mathrm{6}} {x}+…\infty\right)\mathrm{log}_{{e}} \mathrm{2}\right] \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{zero}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$${x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{8}=\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}\:\mathrm{is} \\ $$ Terms of…
Question Number 56413 by gunawan last updated on 16/Mar/19 $$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{1}+{a}+{a}^{\mathrm{2}} +{a}^{\mathrm{3}} +…+{a}^{{x}} =\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{a}^{\mathrm{2}} \right)\left(\mathrm{1}+{a}^{\mathrm{4}} \right) \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{x}\:=\:\_\_\_\_\_. \\ $$ Commented by mr W…
Question Number 56411 by gunawan last updated on 16/Mar/19 $$\mathrm{For}\:\mathrm{a}\:\mathrm{sequence}\:<{a}_{{n}} >\:;\:{a}_{\mathrm{1}} =\mathrm{2},\:\frac{{a}_{{n}+\mathrm{1}} }{{a}_{{n}} }\:=\:\frac{\mathrm{1}}{\mathrm{3}}, \\ $$$$\mathrm{then}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\:{a}_{{r}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 56142 by gunawan last updated on 11/Mar/19 $$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{even}\:\mathrm{and}\:{r}\mathrm{th}\:\mathrm{term}\:\mathrm{has}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{binomial}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}} ,\:\mathrm{then} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 56141 by gunawan last updated on 11/Mar/19 $$\mathrm{If}\:\left(\mathrm{1}+{x}\right)^{{n}} ={C}_{\mathrm{0}} +{C}_{\mathrm{1}} {x}+{C}_{\mathrm{2}} {x}^{\mathrm{2}} +…+{C}_{{n}} {x}^{{n}} ,\:\mathrm{then} \\ $$$$\mathrm{for}\:{n}\:\mathrm{odd},\:{C}_{\mathrm{0}} \:^{\mathrm{2}} −{C}_{\mathrm{1}} \:^{\mathrm{2}} +{C}_{\mathrm{2}} \:^{\mathrm{2}} −{C}_{\mathrm{3}}…
Question Number 56140 by gunawan last updated on 11/Mar/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\: \\ $$$$\mathrm{2}\:{C}_{\mathrm{0}} +\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{2}}{C}_{\mathrm{1}} +\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}}{C}_{\mathrm{2}} +\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{4}}{C}_{\mathrm{3}} +…+\frac{\mathrm{2}^{\mathrm{11}} }{\mathrm{11}}{C}_{\mathrm{10}} \:\:\mathrm{is} \\ $$ Answered by…
Question Number 56139 by gunawan last updated on 11/Mar/19 $$\mathrm{If}\:{x}+{y}=\mathrm{1},\:\mathrm{then}\:\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}^{\mathrm{2}} \:\:^{{n}} {C}_{{r}} \:{x}^{{r}} \:{y}^{{n}−{r}} \:\mathrm{equals} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 56138 by gunawan last updated on 11/Mar/19 $$\mathrm{The}\:\mathrm{pisitive}\:\mathrm{value}\:\mathrm{of}\:\:{a}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{5}} \:\mathrm{and}\:{x}^{\mathrm{15}} \:\mathrm{are}\:\mathrm{equal}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left({x}^{\mathrm{2}} +\:\frac{{a}}{{x}^{\mathrm{3}} }\right)^{\mathrm{10}} \\ $$ Commented by maxmathsup by imad…
Question Number 56137 by gunawan last updated on 11/Mar/19 $$\mathrm{If}\:\left(\mathrm{1}+\mathrm{2}{x}+{x}^{\mathrm{2}} \right)^{{n}} \:=\:\underset{{r}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}\:{a}_{{r}} \:{x}^{{r}} ,\:\mathrm{then}\:{a}_{{r}} = \\ $$ Commented by maxmathsup by imad last…