Question Number 56942 by maxmathsup by imad last updated on 26/Mar/19
![find U_n =∫_1 ^n (([(√(x+1))]−[(√x)])/x^3 ) dx 2) find nature of the serie Σ U_n](https://www.tinkutara.com/question/Q56942.png)
$${find}\:\:{U}_{{n}} =\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{{x}+\mathrm{1}}\right]−\left[\sqrt{{x}}\right]}{{x}^{\mathrm{3}} }\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$