Category: Relation and Functions

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 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 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 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 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…