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 $${let}\:{u}_{{n}} =\:\int_{\mathrm{1}} ^{\infty} \:\:{e}^{−{t}^{{n}} } \:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{n}\rightarrow\infty} \:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:\left({n}\rightarrow\infty\right) \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{radius}\:{of}\:{convergence}\:{of}\:\Sigma\:{u}_{{n}} {x}^{{n}}…
Question Number 31973 by abdo imad last updated on 17/Mar/18 $${let}\:{give}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:\:/\:{u}_{\mathrm{0}} =\mathrm{1}\:{and}\:{u}_{\mathrm{1}} =−\mathrm{1}\:{and} \\ $$$${u}_{{n}+\mathrm{2}} =\:\mathrm{2}{u}_{{n}+\mathrm{1}\:} −{u}_{{n}} \:\:\:.{find}\:{the}\:{radius}\:{of}\:{convegence}\:{for} \\ $$$${this}\:{serie}. \\ $$ Terms of…
Question Number 31966 by abdo imad last updated on 17/Mar/18 $${let}\:{give}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{{n}} }\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{convergence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow\infty} \:\:{I}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \left(−\mathrm{1}\right)^{{n}}…
Question Number 31965 by abdo imad last updated on 17/Mar/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:−\mathrm{2}^{{n}} }{{n}}\:{x}^{{n}} \:\:{with}\:\mid{x}\mid\:<\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31964 by abdo imad last updated on 17/Mar/18 $$\left.\mathrm{1}\right){find}\:\:{S}_{{n}} \:\:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:{C}_{{n}} ^{{k}} \:{sin}\left(\frac{{k}}{{n}}\right) \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:{S}_{{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 31962 by abdo imad last updated on 17/Mar/18 $${let}\:{f}\left({x}\right)=\:\frac{{e}^{\mathrm{2}{x}} }{{x}+\mathrm{1}}\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left({o}\right)\:\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{1}\right)\:. \\ $$ Terms of Service Privacy…