Question Number 32995 by abdo imad last updated on 09/Apr/18 $${let}\:{u}_{\mathrm{0}} ={a}\:,\:{u}_{\mathrm{1}} ={b}\:{and}\:{u}_{{n}+\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}\left({u}_{{n}} \:+{u}_{{n}+\mathrm{1}} \right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{u}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{u}_{{n}} \:\:{if}\:{a}=\mathrm{0} \\ $$$$…
Question Number 32989 by abdo imad last updated on 09/Apr/18 $${let}\:{give}\:{f}\left({x}\right)=\frac{\sqrt{\mathrm{2}+{x}}\:−\sqrt{\mathrm{2}−{x}}\:}{{x}} \\ $$$${find}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\left({f}^{−\mathrm{1}} \left({x}\right)\right)^{'} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32990 by abdo imad last updated on 09/Apr/18 $$\:\:{find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{x}\:{e}^{−{lnx}} \:\:. \\ $$ Commented by prof Abdo imad last updated on 09/Apr/18…
Question Number 32937 by abdo imad last updated on 06/Apr/18 $${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{sin}\left({n}\theta\right)}{{n}}\:{x}^{{n}} \:={arctan}\left(\:\frac{{xsin}\theta}{\mathrm{1}−{xcos}\theta}\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32938 by abdo imad last updated on 06/Apr/18 $${let}\:\mathrm{0}<\theta<\pi\:\:{find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{cos}\left({n}\theta\right)}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{sin}\left({n}\theta\right)}{{n}} \\ $$ Commented by abdo imad last updated…
Question Number 32936 by abdo imad last updated on 06/Apr/18 $${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({n}\theta\right)}{{n}}\:{x}^{{n}} \:=−\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{1}−\mathrm{2}{xcos}\theta+{x}^{\mathrm{2}} \right)\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32935 by abdo imad last updated on 06/Apr/18 $${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} {sin}\left({n}\theta\right)\:=\:\:\frac{{x}\:{sin}\theta}{\mathrm{1}−\mathrm{2}{x}\:{cos}\theta\:+{x}^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32933 by abdo imad last updated on 06/Apr/18 $$\Sigma\:{u}_{{n}} \:{is}\:{a}\:{convergent}\:{serie}\:{with}\:{positif}\:{terms} \\ $$$${find}\:{the}\:{nature}\:{of}\:\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{\sqrt{{u}_{{n}} }}{{n}}\:\:{and}\:\:\:\sum_{{n}\geqslant{o}} \:\:\frac{{u}_{{n}} }{\mathrm{1}+{u}_{{n}} }\:\:. \\ $$ Terms of Service Privacy…
Question Number 32934 by abdo imad last updated on 06/Apr/18 $${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} {cos}\left({n}\theta\right)=\:\frac{{xcos}\theta\:−{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{2}{xcos}\theta\:+{x}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy…
Question Number 32932 by abdo imad last updated on 06/Apr/18 $${find}\:{the}\:{nature}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}}\:. \\ $$ Commented by prof Abdo imad last updated on…