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