Question Number 102883 by bobhans last updated on 11/Jul/20 $${If}\:{x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}\:=\:\mathrm{0}\:{has}\:{the}\:{roots}\:{are}\: \\ $$$$\bar {\alpha}\:\beta\:{and}\:\gamma\:.\:{find}\:{the}\:{value}\:{of} \\ $$$$\alpha\beta^{\mathrm{2}} +\beta\gamma^{\mathrm{2}} +\gamma\alpha^{\mathrm{2}} \:{in}\:{terms}\:{a},{b}\:{and}\:{c} \\ $$ Answered by bemath…
Question Number 37342 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)}\:{x}^{{n}} \:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\mathrm{2}^{{n}} }\:. \\…
Question Number 37339 by math khazana by abdo last updated on 12/Jun/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\:\:\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{1}\:+\mathrm{2}^{\mathrm{3}} \:+\mathrm{3}^{\mathrm{3}} \:+…+{n}^{\mathrm{3}} } \\ $$ Commented by math khazana by…
Question Number 37341 by math khazana by abdo last updated on 12/Jun/18 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\mathrm{3}}{{n}^{\mathrm{2}} \left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by math khazana by abdo…
Question Number 37333 by math khazana by abdo last updated on 12/Jun/18 $${let}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{3}} } \\ $$$$\left.\mathrm{1}\right){study}\:{the}\:{convergence}\:{of}\:{this}\:{serie} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\:\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right){dx}=\mathrm{2}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{4}} }…
Question Number 37334 by math khazana by abdo last updated on 12/Jun/18 $${study}\:{the}\:{convergence}\:{of} \\ $$$$\sum_{{n}=\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} \:\sum_{{k}=\mathrm{0}} ^{\infty} \:\:\frac{{x}^{{k}} }{{k}!}\:. \\ $$ Commented by…
Question Number 37335 by math khazana by abdo last updated on 12/Jun/18 $${find}\:\int\:\:\:\:\:{x}\:{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx}\:. \\ $$ Commented by math khazana by abdo last updated on 14/Jun/18…
Question Number 37295 by math khazana by abdo last updated on 11/Jun/18 $${find}\:{the}\:{principal}\:{value}\:{of}\left\{\left(\mathrm{1}+{i}\right)^{\mathrm{1}−{i}} \right\}^{\mathrm{1}+{i}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 37296 by math khazana by abdo last updated on 11/Jun/18 $${solve}\:{sinz}\:=\mathrm{2}\:\:\:\:\:{zfromC} \\ $$$$ \\ $$ Commented by prof Abdo imad last updated on…
Question Number 37294 by math khazana by abdo last updated on 11/Jun/18 $${let}\:{D}\:={D}\left(\mathrm{0},\mathrm{1}\right)\:{and}\:{f}\left({z}\right)\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{a}_{{n}} {z}^{{n}} \:{is}\:{a}\:{holomorphe} \\ $$$${function}\:/\:\:\mid{f}\left({x}\right)\mid<\:\:\frac{\mathrm{1}}{\mathrm{1}−\mid{z}\mid}\:\:{prove}\:{that} \\ $$$$\mid{a}_{{n}} \mid\leqslant\:\left({n}+\mathrm{1}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \leqslant\left({n}+\mathrm{1}\right){e}. \\ $$…