let-a-n-x-n-with-radius-of-convergence-R-prove-that-R-1-lim-n-sup-n-a-n-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 37355 by math khazana by abdo last updated on 12/Jun/18

let Σ a_n x^n with radius of convergence R prove that R = (1/(lim_(n→+∞) sup^n (√(∣a_n ∣)))) .

$$\:{let}\:\Sigma\:{a}_{{n}} {x}^{{n}} \:\:\:{with}\:{radius}\:{of}\:{convergence}\:{R} \\ $$$${prove}\:{that}\:{R}\:=\:\frac{\mathrm{1}}{{lim}_{{n}\rightarrow+\infty} \:{sup}^{{n}} \sqrt{\mid{a}_{{n}} \mid}}\:\:. \\ $$

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