Question Number 45968 by maxmathsup by imad last updated on 19/Oct/18 $$\left.\mathrm{1}\right){find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{{n}}\:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{sin}\left({nx}\right)}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{cos}\left(\frac{\mathrm{2}{n}\pi}{\mathrm{3}}\right)\:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{sin}\left(\frac{\mathrm{2}{n}\pi}{\mathrm{3}}\right) \\ $$ Commented…
Question Number 45963 by maxmathsup by imad last updated on 19/Oct/18 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}}{\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 45961 by maxmathsup by imad last updated on 19/Oct/18 $${let}\:{f}_{{n}} \left({x}\right)=\left(−\mathrm{1}\right)^{{n}} \:{ln}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{n}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\right)\:{and}\:{f}\left({x}\right)=\Sigma\:{f}_{{n}} \left({x}\right) \\ $$$${find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$ Terms of Service…
Question Number 45962 by maxmathsup by imad last updated on 19/Oct/18 $${study}\:{the}\:{convervence}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\sqrt{{n}+\mathrm{1}}−\sqrt{{n}}}{{nln}\left({n}+\mathrm{1}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 45960 by maxmathsup by imad last updated on 19/Oct/18 $${find}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{x}^{{n}} {sin}\left({nx}\right)}{{n}} \\ $$ Answered by Smail last updated on 22/Oct/18 $${f}\left({x}\right)={Im}\left(\underset{{n}=\mathrm{1}}…
Question Number 45957 by maxmathsup by imad last updated on 19/Oct/18 $${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}!\left({n}−{k}\right)!}\:\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} {u}_{{n}} \\ $$ Commented by maxmathsup by imad last…
Question Number 45792 by maxmathsup by imad last updated on 16/Oct/18 $${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{\left[{k}\right]} }{{k}}\:\:{and}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$$$\left.\mathrm{1}\right){calculate}\:{u}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convergence}\:{of}\:\left({u}_{{n}} \right)…
Question Number 111149 by Aina Samuel Temidayo last updated on 02/Sep/20 $$\mathrm{Let}\:\mathrm{f}_{\mathrm{0}} \left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}\:\mathrm{and}\:\mathrm{f}_{\mathrm{n}} \left(\mathrm{x}\right) \\ $$$$=\mathrm{f}_{\mathrm{0}} \left(\mathrm{f}_{\mathrm{n}−\mathrm{1}} \left(\mathrm{x}\right)\right),\:\mathrm{n}=\mathrm{1},\mathrm{2},\mathrm{3},…\:\mathrm{Evaluate} \\ $$$$\mathrm{f}_{\mathrm{2018}} \left(\mathrm{2018}\right) \\ $$ Commented by…
Question Number 45599 by maxmathsup by imad last updated on 14/Oct/18 $$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{2}{x}+\mathrm{1}−\left[{x}\right]}{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{serie}\:\:\Sigma\:{A}_{{n}} \\ $$ Commented by…
Question Number 45598 by maxmathsup by imad last updated on 14/Oct/18 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{2}} \left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)} \\ $$ Commented by maxmathsup by imad last updated…