Question Number 97617 by mathmax by abdo last updated on 08/Jun/20 $$\mathrm{give}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{2x}\right)}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dx}\:\mathrm{at}\:\mathrm{form}\:\mathrm{of}\:\mathrm{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 32042 by abdo imad last updated on 18/Mar/18 $${let}\:{u}_{{n}} \:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{x}^{{n}} \:{sin}\left(\pi{x}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\Sigma\:{u}_{{n}} \:{converges} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\Sigma\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sint}}{{t}}{dt}\:. \\ $$…
Question Number 32041 by abdo imad last updated on 18/Mar/18 $${find}\:{the}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} \:\:/ \\ $$$${u}_{{n}} =\:\frac{\sqrt{\mathrm{1}}\:+\sqrt{\mathrm{2}}\:+….+\sqrt{{n}}}{{n}^{\mathrm{3}} }\:. \\ $$ Commented by abdo imad last updated on…
Question Number 32037 by abdo imad last updated on 18/Mar/18 $${let}\:\:{u}_{{n}} ={cos}\left(\pi\sqrt{{n}^{\mathrm{2}} \:+{n}+\mathrm{1}}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} . \\ $$$$ \\ $$ Commented by abdo imad last updated on…
Question Number 32036 by abdo imad last updated on 18/Mar/18 $${nature}\:{of}\:\Sigma\:{u}_{{n}} \:\:{with}\:{u}_{{n}} =\:\:\:\frac{\mathrm{1}}{\left({ln}\left(\mathrm{2}\right)\right)^{\mathrm{2}} \:+….+\left({ln}\left({n}\right)\right)^{\mathrm{2}} }\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32033 by abdo imad last updated on 18/Mar/18 $${let}\:{consider}\:{the}\:{sequence}\:\:\left({u}_{{n}} \right)\:\:/{u}_{\mathrm{0}} \in\left[\mathrm{0},\mathrm{1}\right]\:{and} \\ $$$$\forall{n}\in{N}\:\:{u}_{{n}+\mathrm{1}} =\:{u}_{{n}} \:−{u}_{{n}} ^{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{a}\:{simple}\:{equivalent}\:{of}\:\:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{nature}\:{of}\:\Sigma\:{u}_{{n}} . \\ $$…
Question Number 32025 by abdo imad last updated on 18/Mar/18 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}+\mathrm{1}}\:. \\ $$ Commented by abdo imad last updated on 20/Mar/18 $${let}\:{put}\:{S}=\sum_{{n}=\mathrm{0}}…
Question Number 31984 by abdo imad last updated on 17/Mar/18 $${study}\:{the}\:{covergence}\:{of}\:\:\Sigma\:{u}_{{n}} \:\:{with} \\ $$$${u}_{{n}} =^{{n}} \sqrt{\frac{{n}}{{n}+\mathrm{1}}}\:−\mathrm{1}\:\:\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 31981 by abdo imad last updated on 17/Mar/18 $${find}\:{the}\:{nature}\:{of}\:\:\:\sum_{{n}\geqslant\mathrm{2}} \:\frac{\mathrm{1}}{{nln}\left({n}\right)}\:. \\ $$ Commented by abdo imad last updated on 22/Mar/18 $${the}\:{sequence}\:{u}_{{n}} =\:\frac{\mathrm{1}}{{nln}\left({n}\right)}\:{is}\:{decreasing}\:{with}\:{u}_{{n}} \geqslant{o}\:{so}…