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Question Number 33707 by math khazana by abdo last updated on 22/Apr/18

find the radius of convergence for  Σ_(n≥2) ( ∫_(n−(1/2)) ^(n+(1/2))     (dx/(√(x^3 +x +1))))x^n   .

$${find}\:{the}\:{radius}\:{of}\:{convergence}\:{for} \\ $$$$\sum_{{n}\geqslant\mathrm{2}} \left(\:\int_{{n}−\frac{\mathrm{1}}{\mathrm{2}}} ^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} \:\:\:\:\frac{{dx}}{\sqrt{{x}^{\mathrm{3}} +{x}\:+\mathrm{1}}}\right){x}^{{n}} \:\:. \\ $$

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