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…
Question Number 32289 by abdo imad last updated on 22/Mar/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:{ln}\:\left(\:\frac{{e}^{\mathrm{2}{x}} −\mathrm{1}}{{x}}\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32290 by abdo imad last updated on 22/Mar/18 $${let}\:{give}\:{u}_{\mathrm{0}} =\mathrm{1}\:{and}\:{u}_{{n}+\mathrm{1}} =\sqrt{\mathrm{1}+\sqrt{{u}_{{n}} }}\:\:{prove}\:{that}\:{u}_{{n}} \:{is} \\ $$$${increasing}\:. \\ $$ Commented by prof Abdo imad last…
Question Number 32287 by abdo imad last updated on 22/Mar/18 $$\left.\mathrm{1}\right)\:{for}\:{x}>\mathrm{0}\:{prove}\:{that}\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:\leqslant{ln}\left({x}+\mathrm{1}\right)−{lnx}\:\leqslant\:\frac{\mathrm{1}}{{x}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{u}_{{n}} =\:\sum_{{p}=\mathrm{1}} ^{{kn}} \:\frac{\mathrm{1}}{{p}}\:\:\:{find}\:{lim}_{{n}\rightarrow\infty\:} \:{u}_{{n}} . \\ $$ Terms of Service Privacy Policy…
Question Number 32288 by abdo imad last updated on 22/Mar/18 $${study}\:{the}\:{function}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{1}}\:{e}^{\frac{\mathrm{1}}{{x}}} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32284 by abdo imad last updated on 22/Mar/18 $${prove}\:{that}\:\forall\:{x}\in\left[\mathrm{0},\frac{\pi}{\mathrm{4}}\right]\:\:{x}\leqslant{tanx}\leqslant\mathrm{2}{x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\alpha_{{n}} \:{and}\:\beta_{{n}} \:{from}\:{R}\:/\:\:\alpha_{{n}} \leqslant\:\sum_{{k}=\mathrm{2}} ^{{n}} \:{tan}\left(\frac{\pi}{\mathrm{2}{n}}\right)\leqslant\:\beta_{{n}} \\ $$ Terms of Service Privacy Policy…