Question Number 77528 by Mohamed Amine Bouguezzoul last updated on 07/Jan/20 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{k}^{\alpha} }{\mathrm{2}^{{k}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 11991 by FilupS last updated on 09/Apr/17 $$\mathrm{show}\:\mathrm{that}: \\ $$$$\frac{\mathrm{2}{n}}{\mathrm{2}{n}+\mathrm{1}}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}} \\ $$$$\mathrm{via}\:\mathrm{power}\:\mathrm{series},\:\mathrm{and}\:\mathrm{other}\:\mathrm{methods} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143063 by ERA last updated on 09/Jun/21 $$\boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\pi}}{\mathrm{2n}+\mathrm{1}}\right)\boldsymbol{\mathrm{cos}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{2n}+\mathrm{1}}\right)\boldsymbol{\mathrm{cos}}\left(\frac{\mathrm{3}\boldsymbol{\pi}}{\mathrm{2n}+\mathrm{1}}\right)…..\boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{n}\pi}}{\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{2}^{\boldsymbol{\mathrm{n}}} } \\ $$$$\boldsymbol{\mathrm{prove}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77524 by BK last updated on 07/Jan/20 Commented by lémùst last updated on 07/Jan/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{question}\:? \\ $$ Commented by BK last updated on…
Question Number 11988 by tawa last updated on 08/Apr/17 Commented by tawa last updated on 09/Apr/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this}.\:\mathrm{Thanks}\:\mathrm{in}\:\mathrm{advance}.\:\mathrm{16a},\:\mathrm{16b},\:\mathrm{17a} \\ $$ Commented by tawa last updated on…
Question Number 143057 by ERA last updated on 09/Jun/21 $$\mathrm{cos}\left(\boldsymbol{\alpha}\right)×\mathrm{cos}\left(\mathrm{2}\alpha\right)×\mathrm{cos}\left(\mathrm{4}\alpha\right)×….×\mathrm{cos}\left(\mathrm{2}^{\mathrm{n}} \boldsymbol{\alpha}\right)=\frac{\boldsymbol{\mathrm{sin}}\left(\mathrm{2}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \boldsymbol{\alpha}\right)}{\mathrm{2}^{\mathrm{n}+\mathrm{1}} \mathrm{sin}\left(\alpha\right)} \\ $$$$\boldsymbol{\mathrm{prove}} \\ $$ Answered by Dwaipayan Shikari last updated on 09/Jun/21…
Question Number 11987 by tawa last updated on 08/Apr/17 $$\mathrm{The}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{moon}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{4}},\:\mathrm{and}\:\mathrm{its}\:\mathrm{mass}\:\mathrm{is}\:\:\frac{\mathrm{1}}{\mathrm{81}}\:\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\:\mathrm{on}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{is}\:\mathrm{9}.\mathrm{8m}/\mathrm{s}^{\mathrm{2}} .\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{its}\:\mathrm{value}\:\mathrm{on}\:\mathrm{the}\:\mathrm{moon}'\mathrm{s}\:\mathrm{surface}. \\ $$ Answered by ajfour last updated on 09/Apr/17 $${g}_{{e}}…
Question Number 77523 by MJS last updated on 07/Jan/20 $$\mathrm{how}\:\mathrm{many}\:\mathrm{silly}\:\mathrm{questions}\:\mathrm{can}\:\mathrm{a}\:\mathrm{person}\:\mathrm{ask} \\ $$$$\mathrm{within}\:\mathrm{the}\:\mathrm{first}\:\delta\:\mathrm{days}\:\mathrm{of}\:\mathrm{the}\:\mathrm{year}\:\psi\:\mathrm{when} \\ $$$$\mathrm{the}\:\mathrm{number}\:\chi_{\mathrm{0}} \:\mathrm{of}\:\mathrm{his}\:\mathrm{IDs}\notin\mathbb{R}\:\mathrm{in}\:\mathrm{the}\:\mathrm{year}\:\psi−\mathrm{1} \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\left[\mathrm{ln}\:\left(\frac{\psi}{\mathrm{2}}+\mathrm{3}\mathbb{M}\right)\right]\leqslant\chi_{\mathrm{0}} <\underset{{q}_{\mathrm{0}} ,\:{x}\rightarrow\infty} {\mathrm{lim}}\frac{{q}_{\mathrm{0}} ^{{x}} \sqrt{\mathrm{2}\pi{x}}}{\mathrm{e}^{{q}_{\mathrm{0}} } } \\…
Question Number 11982 by tawa last updated on 08/Apr/17 $$\int\mathrm{x}^{\mathrm{5}} \left(\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}}\right)\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 08/Apr/17 $${I}=\frac{\mathrm{1}}{\mathrm{3}}\int{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:\left(\mathrm{3}{x}^{\mathrm{2}} {dx}\right)…
Question Number 77514 by liki last updated on 07/Jan/20 Answered by jagoll last updated on 07/Jan/20 $${L}_{\mathrm{1}} :\:{y}=−\frac{\mathrm{3}}{\mathrm{4}}\left({x}−\mathrm{2}\right)+\left(−\mathrm{1}\right) \\ $$$${L}_{\mathrm{1}} :\:{y}\:=\:−\frac{\mathrm{3}}{\mathrm{4}}{x}+\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:{a}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${let}\:{poin}\:{C}\left({x},{y}\right)\:,\:{CA}\:{perpendicular} \\ $$$${to}\:{L}_{\mathrm{1}}…