Question Number 33707 by math khazana by abdo last updated on 22/Apr/18
$${find}\:{the}\:{radius}\:{of}\:{convergence}\:{for} \\ $$$$\sum_{{n}\geqslant\mathrm{2}} \left(\:\int_{{n}−\frac{\mathrm{1}}{\mathrm{2}}} ^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} \:\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{3}} +{x}\:+\mathrm{1}}}\right){x}^{{n}} \:\:. \\ $$