Question Number 11262 by 786786AM last updated on 18/Mar/17 $$\mathrm{The}\:\mathrm{k}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{K},\:\mathrm{the}\:\mathrm{m}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\:\mathrm{M}\:\mathrm{and}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\mathrm{N}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{geometic}, \\ $$$$\left(\mathrm{m}−\mathrm{n}\right)\:\mathrm{log}\:\mathrm{K}\:+\:\left(\mathrm{n}−\mathrm{k}\right)\:\mathrm{log}\:\mathrm{M}\:+\:\left(\mathrm{k}−\mathrm{m}\right)\:\mathrm{log}\:\mathrm{N}\:=\:\mathrm{0}.\: \\ $$ Answered by mrW1 last updated on 20/Mar/17 $${K}={a}\centerdot{q}^{{k}−\mathrm{1}}…
Question Number 11256 by 786786AM last updated on 18/Mar/17 $$\mathrm{In}\:\mathrm{the}\:\mathrm{arithmetic}\:\mathrm{progression},\:\mathrm{u}_{\mathrm{1}\:} =\mathrm{1}.\mathrm{Given}\:\mathrm{that}\:\mathrm{u}_{\mathrm{7}\:} ,\:\mathrm{u}_{\mathrm{11}} \mathrm{and}\:\mathrm{u}_{\mathrm{17}} \:\mathrm{are}\:\mathrm{in}\:\mathrm{geometric}\: \\ $$$$\mathrm{progression},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{each}. \\ $$ Answered by ajfour last updated on 18/Mar/17…
Question Number 11255 by 786786AM last updated on 18/Mar/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{4}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.,\:\mathrm{is}\:\mathrm{p},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{8}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{12}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{r},\:\mathrm{express}\:\left(\mathrm{3p}+\mathrm{r}\right)\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{q}. \\ $$ Answered by ajfour last updated on 18/Mar/17 $$\mathrm{p}=\mathrm{2}\left(\mathrm{2a}+\mathrm{3d}\right) \\ $$$$\mathrm{q}=\mathrm{4}\left(\mathrm{2a}+\mathrm{7d}\right) \\…
Question Number 142301 by 777316 last updated on 29/May/21 Answered by Dwaipayan Shikari last updated on 29/May/21 $$\mathrm{sin}\:\left(\frac{\pi{s}}{\mathrm{2}}\right)\Gamma\left(\mathrm{1}−{s}\right)=\mathrm{sin}\:\left(\frac{\pi{s}}{\mathrm{2}}\right)\frac{\pi}{{sin}\left(\pi{s}\right)\Gamma\left({s}\right)} \\ $$$$\underset{{s}\rightarrow\mathrm{2}{n}} {\mathrm{lim}}=\frac{\pi}{\mathrm{2cos}\:\left(\frac{\pi}{\mathrm{2}}{s}\right)\Gamma\left({s}\right)}=\frac{\pi}{\mathrm{2}\Gamma\left(\mathrm{2}{n}\right)\left(−\mathrm{1}\right)^{{n}} } \\ $$ Terms…
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Question Number 76726 by Rio Michael last updated on 29/Dec/19 $$\:\mathrm{var}\left(\mathrm{x}\right)\:=\:\mathrm{2}\:\mathrm{then}\:\mathrm{var}\left(\mathrm{2x}\:−\mathrm{3}\right)=? \\ $$$$\mathrm{E}\left(\mathrm{x}\right)\:=\:\mathrm{2}\:\mathrm{then}\:\mathrm{E}\left(\mathrm{2x}\:−\mathrm{3}\right)\:=\:? \\ $$ Answered by john santu last updated on 30/Dec/19 $${E}\left({x}\right)=\underset{{x}} {\sum}{xf}\left({x}\right)=\mathrm{2}\:…
Question Number 76724 by Rio Michael last updated on 29/Dec/19 $$\int_{\mathrm{0}} ^{\mathrm{3}} \mid\mathrm{x}^{\mathrm{2}} −\mathrm{1}\mid\:\mathrm{dx}\:\equiv\: \\ $$ Commented by abdomathmax last updated on 30/Dec/19 $$\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 76723 by Rio Michael last updated on 29/Dec/19 $$\mathrm{the}\:\mathrm{maclaurin}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{ln}\:\left(\mathrm{3}\:+\:\mathrm{4}{x}\right)\:{is}\:{valid}\:{for} \\ $$$$\left.{A}\right)\:\:−\frac{\mathrm{3}}{\mathrm{4}}\:\leqslant\:\mathrm{x}<\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\left.\mathrm{B}\right)\:−\frac{\mathrm{3}}{\mathrm{4}}<\:\mathrm{x}\:\leqslant\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\left.\mathrm{C}\right)\:−\frac{\mathrm{1}}{\mathrm{4}}<\:\mathrm{x}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{D}\right)\:−\frac{\mathrm{3}}{\mathrm{4}}<\:\mathrm{x}\:<\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$ Terms of Service Privacy…
Question Number 76680 by Tony Lin last updated on 29/Dec/19 $${prove}\:{that}: \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} {dx} \\ $$ Commented by…
Question Number 142207 by 777316 last updated on 27/May/21 Answered by mr W last updated on 28/May/21 $${say}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{a}_{{n}} ={L} \\ $$$${L}=\frac{\mathrm{3}{L}+\mathrm{4}}{\mathrm{2}{L}+\mathrm{3}} \\ $$$$\mathrm{2}{L}^{\mathrm{2}} +\mathrm{3}{L}=\mathrm{3}{L}+\mathrm{4}…