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let-u-n-0-1-x-n-artan-nx-dx-1-lim-u-n-2-nature-of-u-n-3-calculate-u-n-4-equivalent-of-u-n-




Question Number 174938 by Mathspace last updated on 14/Aug/22
let u_n = ∫_0 ^1 x^n artan(nx)dx  1)lim u_n ?  2)nature of Σ u_n   3) calculate u_n   4)equivalent of u_n ?
$${let}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} {artan}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right){lim}\:{u}_{{n}} ? \\ $$$$\left.\mathrm{2}\right){nature}\:{of}\:\Sigma\:{u}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{u}_{{n}} \\ $$$$\left.\mathrm{4}\right){equivalent}\:{of}\:{u}_{{n}} ? \\ $$

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