Question Number 133432 by Dwaipayan Shikari last updated on 22/Feb/21 $$\frac{{sin}\sqrt{\pi}}{\mathrm{1}^{\mathrm{3}} }+\frac{{sin}\sqrt{\mathrm{4}\pi}}{\mathrm{2}^{\mathrm{3}} }+\frac{{sin}\sqrt{\mathrm{9}\pi}}{\mathrm{3}^{\mathrm{3}} }+\frac{{sin}\sqrt{\mathrm{16}\pi}}{\mathrm{4}^{\mathrm{3}} }+….=\frac{\pi\sqrt{\pi}}{\mathrm{12}}\left(\mathrm{1}−\mathrm{3}\sqrt{\pi}+\mathrm{2}\pi\right) \\ $$ Answered by mindispower last updated on 24/Feb/21 $$\underset{{n}\geqslant\mathrm{0}}…
Question Number 67898 by ramirez105 last updated on 01/Sep/19 $$ \\ $$$${differential}\:{equation}. \\ $$$${homogenous}. \\ $$$$ \\ $$$${ydx}+\left(\mathrm{2}{x}+\mathrm{3}{y}\right){dy}=\mathrm{0} \\ $$$$ \\ $$ Terms of Service…
Question Number 2362 by 123456 last updated on 18/Nov/15 $${f}:\mathbb{C}\rightarrow\mathbb{C},\left({a},{b}\right)\in\mathbb{R}^{\mathrm{2}} ,{a}<{b} \\ $$$${f}\left({z}−{a}\right)={f}\left({b}−{z}\right)\mathrm{sin}\:\frac{{z}\pi}{{b}−{a}} \\ $$$${f}\left({z}\right)={z}^{\mathrm{2}} ,\Re\left({z}\right)\geqslant\frac{{a}+{b}}{\mathrm{2}} \\ $$$${f}\left({z}\right)=\mathrm{0},{z}=? \\ $$ Commented by Rasheed Soomro last…
Question Number 2355 by 123456 last updated on 17/Nov/15 $$\frac{{df}}{{d}\zeta}\mathrm{sinh}\:\zeta+\frac{{df}}{{d}\theta}\mathrm{sin}\:\theta+\frac{{df}}{{d}\rho}\rho=\mathrm{0} \\ $$$${f}\left(\rho,\zeta,\theta\right)=?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2358 by 123456 last updated on 18/Nov/15 $${a}_{{n}+\mathrm{1}} =−\frac{{a}_{{n}} \left(\mid{a}_{{n}} \mid+\mathrm{1}\right)}{\mid{a}_{{n}} \mid},{a}_{\mathrm{1}} =\mathrm{1} \\ $$$${b}_{{n}+\mathrm{1}} ={b}_{{n}} +{a}_{{n}+\mathrm{1}} ,{b}_{\mathrm{1}} ={a}_{\mathrm{1}} \\ $$$${b}_{\mathrm{10}} =? \\…
Question Number 133394 by Dwaipayan Shikari last updated on 21/Feb/21 Commented by Dwaipayan Shikari last updated on 21/Feb/21 $${Three}\:{indentical}\:{point}\:{charges}\:,\:{each}\:{of}\:{mass}\:\boldsymbol{{m}}\:{and}\:{charge} \\ $$$$\boldsymbol{{Q}}\:,{hanging}\:{from}\:{three}\:{strings}\:.{Find}\:{the}\:{value}\:{of}\:\boldsymbol{{Q}}\:{in}\:{terms} \\ $$$${of}\:\boldsymbol{{m}},\boldsymbol{{L}}\:{and}\:\boldsymbol{\theta}\:\left({They}\:{are}\:{in}\:{equilibrium}\right) \\ $$…
Question Number 133381 by Dwaipayan Shikari last updated on 21/Feb/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\left(\frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}\right)+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\right)+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}\right)+…=\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2289 by 123456 last updated on 14/Nov/15 $$\mathrm{suppose}\:\mathrm{that}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R},\:\mathrm{lets}\:{f}\in\mathrm{C}^{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{suppose}\:\mathrm{that}\:\exists\alpha\in\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left(\alpha\right)+{f}\left(\mathrm{1}−\alpha\right)=\mathrm{1} \\ $$$$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$$$\exists\xi\in\left[\mathrm{0},\mathrm{1}\right],{f}\left(\xi\right)=\xi \\ $$ Commented by Rasheed Soomro last…
Question Number 67820 by angezbcn last updated on 31/Aug/19 $${x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{6}{x} \\ $$ Commented by mr W last updated on 01/Sep/19 $$={x}\left({x}^{\mathrm{2}} −{x}−\mathrm{6}\right) \\…
Question Number 133344 by Dwaipayan Shikari last updated on 21/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\frac{{n}}{\pi}\right)}{{n}^{\mathrm{4}} }=−\frac{\mathrm{1}}{\mathrm{48}\pi^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{12}}\left(\mathrm{1}−\frac{\mathrm{1}}{\pi^{\mathrm{2}} }\right)+\frac{\pi^{\mathrm{4}} }{\mathrm{90}} \\ $$ Terms of Service Privacy Policy Contact:…