Category: Relation and Functions

Question Number 28616 by abdo imad last updated on 27/Jan/18 $${let}\:{give}\:{u}_{{n}} =\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \:−{e}\:\:\:{find}\:{nature}\:{of}\:\:\Sigma\:{u}_{{n}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 28542 by abdo imad last updated on 26/Jan/18 $${if}\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}−{x}−{y}−{xy}}\:=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:{g}_{{n}} \left({y}\right)\:{x}^{{n}} \:\:{find}\:{g}_{{n}} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 28537 by abdo imad last updated on 26/Jan/18 $${prove}\:{that}\:\:\:\forall\:{n}\in\:\mathbb{N} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\left({n}+\mathrm{1}\right)^{\mathrm{2}} }}\:\leqslant\:{argsh}\left({n}+\mathrm{1}\right)\:−{argsh}\left({n}\right)\leqslant\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{n}^{\mathrm{2}} }}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 28536 by abdo imad last updated on 26/Jan/18 $${study}\:{the}\:{convergence}\:{of}\:\:{V}_{{n}} =\:\prod_{\mathrm{1}\leqslant{p}\leqslant{n}} \left(\mathrm{1}\:+\frac{{i}}{{p}}\right) \\ $$$${i}\in\:{C}\:{and}\:{i}^{\mathrm{2}} =−\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 28531 by abdo imad last updated on 26/Jan/18 $${let}\:{give}\:\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{k}^{{p}} \:\:\:\:,\:{p}\in{N}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$$${find}\:{the}\:{radius}\:{of}\:{convergence}\:{of}\:{the}\:{serie}\:\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{{x}^{{n}} }{{S}_{{n}} }\:. \\ $$ Terms of Service…