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find-radous-of-conbergence-for-theserie-n-0-x-n-




Question Number 33846 by prof Abdo imad last updated on 26/Apr/18
find radous of conbergence for theserie Σ_(n≥0) x^(n!) .
$${find}\:{radous}\:{of}\:{conbergence}\:{for}\:{theserie}\:\sum_{{n}\geqslant\mathrm{0}} {x}^{{n}!} .\: \\ $$
Commented by prof Abdo imad last updated on 31/May/18
Σ_(n=0) ^∞  x^(n!)  is a extract serie from the serie  Σ_(n=0) ^(+∞)  x^n   wich converges if ∣x∣<1  so R ≤1 .
$$\sum_{{n}=\mathrm{0}} ^{\infty} \:{x}^{{n}!} \:{is}\:{a}\:{extract}\:{serie}\:{from}\:{the}\:{serie} \\ $$$$\sum_{{n}=\mathrm{0}} ^{+\infty} \:{x}^{{n}} \:\:{wich}\:{converges}\:{if}\:\mid{x}\mid<\mathrm{1}\:\:{so}\:{R}\:\leqslant\mathrm{1}\:. \\ $$

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