Question Number 94148 by abdomathmax last updated on 17/May/20 $${solve}\:{cosz}\:={e}^{{z}} \:\:\:\:\:{zfrom}\:{C} \\ $$ 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 28538 by abdo imad last updated on 26/Jan/18 $${study}\:{the}\:{convergence}\:{of} \\ $$$${u}_{{n}\:} \:\:=\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{k}^{\mathrm{2}} }}\:\:−{argsh}\left({n}\right)\:\:{and} \\ $$$${v}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{k}^{\mathrm{2}} }}\:\:. \\ $$$$…
Question Number 28537 by abdo imad last updated on 26/Jan/18 $${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 28535 by abdo imad last updated on 26/Jan/18 $${study}\:{the}\:{convergence}\:{of}\:\:{U}_{{n}} =\:\left(\mathrm{1}+\frac{{z}}{{n}}\right)^{{n}} \:{with}\:{z}\in{C}\:. \\ $$ 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 28530 by abdo imad last updated on 26/Jan/18 $${prove}\:{that}\:\mid{sinx}\mid=\:\frac{\mathrm{8}}{\pi}\:\sum_{{n}=\mathrm{1}} ^{+\infty} \:\frac{{sin}^{\mathrm{2}} \left({nx}\right)}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$ 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…
Question Number 28436 by abdo imad last updated on 25/Jan/18 $${study}\:{the}\:{nature}\:{of}\:{sequence}\:\left({u}_{{n}} \right)\:/\:{u}_{\mathrm{0}} =\mathrm{1}\:{and} \\ $$$${u}_{{n}+\mathrm{1}} =\:\:\frac{\mathrm{1}}{{u}_{{n}\:} +\:{e}^{−{n}} }\:. \\ $$ Terms of Service Privacy Policy…
Question Number 28428 by abdo imad last updated on 25/Jan/18 $${let}\:{give}\:{f}_{{n}} \left({x}\right)=\:\left(\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} \right)^{\left({n}\right)} \:\:\:{find}\:\:{f}_{{n}} \:. \\ $$ Commented by abdo imad last updated on…