Question Number 34690 by math khazana by abdo last updated on 09/May/18
$${let}\:{U}_{{n}} =\frac{\mathrm{1}}{{n}!}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left({arcsinx}\right)^{{n}} {dx} \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \:. \\ $$