Question Number 94331 by mathmax by abdo last updated on 18/May/20 $$\left.\mathrm{1}\right)\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{x}^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}…
Question Number 94318 by john santu last updated on 18/May/20 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{xy}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\:\mathrm{and}\: \\ $$$$\mathrm{f}\left(\mathrm{7}\right)\:=\:\mathrm{7}.\:\mathrm{find}\:\mathrm{f}\left(\mathrm{1008}\right)\: \\ $$ Commented by Rasheed.Sindhi last updated on 18/May/20 $${f}\left(\mathrm{7}\right)={f}\left(\mathrm{7}×\mathrm{1}\right)={f}\left(\mathrm{7}+\mathrm{1}\right)=\mathrm{7} \\ $$$${f}\left(\mathrm{8}\right)=\mathrm{7}…
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Question Number 28616 by abdo imad last updated on 27/Jan/18 $${let}\:{give}\:{u}_{{n}} =\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \:−{e}\:\:\:{find}\:{nature}\:{of}\:\:\Sigma\:{u}_{{n}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 94148 by abdomathmax last updated on 17/May/20 $${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