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 $${the}\:{sequence}\:{u}_{{n}} =\:\frac{\mathrm{1}}{{nln}\left({n}\right)}\:{is}\:{decreasing}\:{with}\:{u}_{{n}} \geqslant{o}\:{so}…
Question Number 31982 by abdo imad last updated on 17/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)}\:. \\ $$ Commented by 6123 last updated on 18/Mar/18 $$\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 31983 by abdo imad last updated on 17/Mar/18 $${calculate}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{n}^{\mathrm{2}} \:−\mathrm{2}}{{n}!}\:\:. \\ $$ Commented by prakash jain last updated on 18/Mar/18 $${n}^{\mathrm{2}}…
Question Number 31979 by abdo imad last updated on 17/Mar/18 $${calculate}\:\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\:\frac{\mathrm{1}}{\left({n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} }\:\:. \\ $$ Commented by abdo imad last updated on 22/Mar/18…
Question Number 31980 by abdo imad last updated on 17/Mar/18 $${let}\:−\mathrm{1}<{x}<\mathrm{1}\:{calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{x}^{{n}} }{\left(\mathrm{1}−{x}^{{n}} \right)\left(\mathrm{1}−{x}^{{n}+\mathrm{1}} \right)}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31978 by abdo imad last updated on 17/Mar/18 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)\left(\mathrm{2}{n}+\mathrm{5}\right)}. \\ $$ Answered by Joel578 last updated on 18/Mar/18 $${S}_{{k}} \:=\:\underset{{n}=\mathrm{0}} {\overset{{k}}…
Question Number 31977 by abdo imad last updated on 17/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)} \\ $$ Commented by Tinkutara last updated on 17/Mar/18 $$\frac{\mathrm{1}}{\mathrm{2}} \\ $$…
Question Number 31976 by abdo imad last updated on 17/Mar/18 $${let}\:{u}_{{n}} =^{{n}+\mathrm{1}} \sqrt{{n}+\mathrm{1}}\:−\:^{{n}} \sqrt{{n}}\:\:{find}\:{radius}\:{of}\:{convergence}\: \\ $$$${for}\:\:\Sigma\:{u}_{{n}} {z}^{{n}} \:\:\:\:\left({z}\in{C}\right). \\ $$ Terms of Service Privacy Policy…
Question Number 31975 by abdo imad last updated on 17/Mar/18 $${let}\:{u}_{{n}} =\:\int_{\mathrm{1}} ^{\infty} \:\:{e}^{−{t}^{{n}} } \:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{n}\rightarrow\infty} \:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:\left({n}\rightarrow\infty\right) \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{radius}\:{of}\:{convergence}\:{of}\:\Sigma\:{u}_{{n}} {x}^{{n}}…