let-u-n-1-e-t-n-dt-1-calculate-lim-n-u-n-2-find-a-equivalent-of-u-n-n-3-find-the-radius-of-convergence-of-u-n-x-n-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 31975 by abdo imad last updated on 17/Mar/18

let u_n = ∫_1 ^∞ e^(−t^n ) dt 1) calculate lim_(n→∞) u_n 2)find a equivalent of u_n (n→∞) 3)find the radius of convergence of Σ u_n x^n .

$${let}\:{u}_{{n}} =\:\int_{\mathrm{1}} ^{\infty} \:\:{e}^{−{t}^{{n}} } \:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{n}\rightarrow\infty} \:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:\left({n}\rightarrow\infty\right) \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{radius}\:{of}\:{convergence}\:{of}\:\Sigma\:{u}_{{n}} {x}^{{n}} . \\ $$

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let-u-n-1-e-t-n-dt-1-calculate-lim-n-u-n-2-find-a-equivalent-of-u-n-n-3-find-the-radius-of-convergence-of-u-n-x-n-

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