Question Number 32346 by abdo imad last updated on 23/Mar/18 $${let}\:{u}_{\mathrm{0}} =\mathrm{1}\:{and}\:\:{u}_{{n}+\mathrm{1}} =\:{u}_{{n}} \:\frac{\mathrm{1}+\mathrm{2}{u}_{{n}} }{\mathrm{1}+\mathrm{3}{n}} \\ $$$${give}\:{a}\:{equivalent}\:{of}\:{u}_{{n}\:} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32348 by abdo imad last updated on 23/Mar/18 $$\left.\mathrm{1}\right){let}\:{n}\:\in{Nand}\:\:\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}+{cos}^{\mathrm{2}} \left({nx}\right)}\:.{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{f}\in\:{C}^{\mathrm{0}} \left(\left[\mathrm{0},\pi\right],\:{R}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{f}\left({x}\right)}{\mathrm{1}+{cos}^{\mathrm{2}} \left({nx}\right)}{dx}\:. \\ $$ Terms…
Question Number 32344 by abdo imad last updated on 23/Mar/18 $${let}\:\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{ch}\left(\frac{\mathrm{1}}{\:\sqrt{{k}+{n}}}\right)\:−{n} \\ $$$${prove}\:{that}\:{u}_{{n}} \:{is}\:{convergent}\:{and}\:{find}\:{its}\:{limit}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32335 by abdo imad last updated on 23/Mar/18 $${let}\:{t}\geqslant\mathrm{0}\:{and}\:{f}\left({t}\right)\:=\frac{{t}}{\:\sqrt{\mathrm{1}+{t}}}\:.{prove}\:{that}\:{the}\:{sequence} \\ $$$${S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:\:{converges}\:{and}\:{find}\:{its}\:{limit}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32303 by abdo imad last updated on 22/Mar/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{\mathrm{2}{n}+{k}}\:\:. \\ $$ Commented by abdo imad last updated on 01/Apr/18 $${let}\:{put}\:{S}_{{n}}…
Question Number 32300 by abdo imad last updated on 22/Mar/18 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} {n}^{\mathrm{2}} \:{e}^{{in}\theta} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{n}^{\mathrm{2}} {cos}\left({n}\theta\right)\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{n}^{\mathrm{2}} {sin}\left({n}\theta\right)=. \\ $$ Terms…
Question Number 32299 by abdo imad last updated on 22/Mar/18 $${find}\:{tbe}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{{e}^{\frac{\mathrm{1}}{{n}}} \:\:+{e}^{−\frac{\mathrm{1}}{{n}}} }{{n}}\:. \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32295 by abdo imad last updated on 22/Mar/18 $${calculate}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(\mathrm{2}{k}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{k}} \:\:. \\ $$ Commented by prof Abdo imad last updated on 04/Apr/18…
Question Number 32293 by abdo imad last updated on 22/Mar/18 $${let}\:{u}_{\mathrm{0}} =\:\sqrt{\mathrm{3}}\:\:{and}\:{u}_{{n}+\mathrm{1}} =\sqrt{\mathrm{2}+{u}_{{n}} ^{\mathrm{2}} } \\ $$$${calculate}\:{u}_{{n}} \:{interms}\:{of}\:{n}. \\ $$ Commented by abdo imad last…
Question Number 32294 by abdo imad last updated on 22/Mar/18 $${let}\:{u}_{\mathrm{1}} =\mathrm{1}\:{and}\:{u}_{\mathrm{2}} =\mathrm{2}\:{and}\:{u}_{{n}} ={u}_{{n}−\mathrm{1}} \:+{u}_{{n}−\mathrm{2}} \\ $$$${find}\:{u}_{{n}} \:{interms}\:{of}\:{n}\:. \\ $$ Commented by Tinkutara last updated…