Question Number 41513 by maxmathsup by imad last updated on 08/Aug/18 $${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}^{\mathrm{2}} } {cos}\left({x}^{\mathrm{2}} \right)\:{dx}\:\:{and}\:\:{B}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}^{\mathrm{2}} } {sin}\left({x}^{\mathrm{2}} \right){dx}\:\:\:\:\left({n}\in\:{N}^{\bigstar} \right)…
Question Number 41410 by maxmathsup by imad last updated on 06/Aug/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\left[{ne}^{−{x}} \right]{dx}\:\:{with}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\sum_{{n}\geqslant\mathrm{2}} \:\:\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\:\Sigma\:\frac{\mathrm{1}}{{A}_{{n}} }\:\:{and}\:\Sigma\:\frac{\mathrm{1}}{{A}_{{n}} ^{\mathrm{2}}…
Question Number 41408 by maxmathsup by imad last updated on 06/Aug/18 $${calculate}\:\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 41409 by maxmathsup by imad last updated on 06/Aug/18 $${calculate}\:{S}_{{p}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)…\left({n}+{p}\right)}\:\:{with}\:{p}\:{fromN} \\ $$ Answered by sma3l2996 last updated on 07/Aug/18…
Question Number 41407 by maxmathsup by imad last updated on 06/Aug/18 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 41349 by math khazana by abdo last updated on 06/Aug/18 $${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{3}{n}−\mathrm{1}} \\ $$ Commented by maxmathsup by imad last updated…
Question Number 41345 by maxmathsup by imad last updated on 05/Aug/18 $${let}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\:−{ln}\left({n}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\left({u}_{{n}} \right){is}\:{convergent} \\ $$$$\left.\mathrm{2}\right)\:{let}\:\gamma\:={lim}_{{n}\rightarrow+\infty} {u}_{{n}} \:\:\:{prove}\:{that}\:\mathrm{0}<\gamma<\mathrm{1}\:\: \\ $$ Commented…
Question Number 41342 by maxmathsup by imad last updated on 05/Aug/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} \left({n}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 41286 by maxmathsup by imad last updated on 04/Aug/18 $${find}\:\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{interms}\:{of}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Terms of Service Privacy Policy…
Question Number 41236 by maxmathsup by imad last updated on 04/Aug/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\:\frac{\mathrm{3}{n}^{\mathrm{2}} \:+\mathrm{1}}{\left({n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…