Question Number 43260 by maxmathsup by imad last updated on 08/Sep/18 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} \:−\mathrm{1}}\:. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 108711 by mathmax by abdo last updated on 18/Aug/20 $$\mathrm{calculate}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\left(−\mathrm{1}\right)^{\mathrm{2}\left[\mathrm{x}\right]−\mathrm{1}} \mathrm{cos}\left(\mathrm{n}\left[\mathrm{x}\right]\right)\mathrm{dx} \\ $$$$\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$ Answered by mathmax by abdo…
Question Number 108706 by mathmax by abdo last updated on 18/Aug/20 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \left(\mathrm{n}^{\mathrm{2}} −\mathrm{n}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{n}^{\mathrm{2}} +\mathrm{3n}+\mathrm{2}\right)}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 108705 by mathmax by abdo last updated on 18/Aug/20 $$\mathrm{if}\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\mathrm{u}_{\mathrm{k}} =\mathrm{n}\left(\mathrm{2}^{\mathrm{n}} +\mathrm{3}\right)\:\:\mathrm{determine}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\mathrm{u}_{\mathrm{k}} } \\ $$ Answered by mathmax…
Question Number 108688 by abdomsup last updated on 18/Aug/20 $${prove}\:{that}\: \\ $$$$\sum_{{n}=−\infty} ^{\infty} \:\frac{\mathrm{1}}{\left({ax}+\mathrm{1}\right)^{{n}} } \\ $$$$=−\frac{\pi}{{a}^{{n}} }\:{lim}_{{x}\rightarrow−\frac{\mathrm{1}}{{a}}} \:\:\:\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)!}\left\{{cotan}\left(\pi{x}\right)\right\}^{\left({n}−\mathrm{1}\right)} \\ $$ Commented by mathdave last…
Question Number 108547 by 1549442205PVT last updated on 17/Aug/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation}: \\ $$$$\mathrm{cosz}\:=\mathrm{2} \\ $$ Answered by mr W last updated on 17/Aug/20 $${e}^{{zi}} =\mathrm{cos}\:{z}+{i}\:\mathrm{sin}\:{z} \\…
Question Number 43007 by abdo.msup.com last updated on 06/Sep/18 $${calculate}\: \\ $$$${A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:{C}_{{n}} ^{{k}} \\ $$$${B}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \\ $$$${C}_{{n}}…
Question Number 43001 by abdo.msup.com last updated on 06/Sep/18 $${prove}\:{that}\:\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{\mathrm{1}}{{k}}\right)>\mathrm{1}+\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $${LHS} \\…
Question Number 43003 by abdo.msup.com last updated on 06/Sep/18 $${let}\:{u}_{{n}} =\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\frac{\mathrm{1}}{\:\sqrt{{ij}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} \:{u}_{{n}} \\ $$ Answered by maxmathsup by imad last…
Question Number 43000 by abdo.msup.com last updated on 06/Sep/18 $${prove}\:{that}\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+….+\sqrt{\mathrm{2}}}}\:\:=\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right) \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18 $${cos}\mathrm{2}\alpha=\mathrm{2}{cos}^{\mathrm{2}} \alpha−\mathrm{1} \\ $$$${cos}^{\mathrm{2}} \alpha=\frac{\mathrm{1}+{cos}\mathrm{2}\alpha}{\mathrm{2}}…