For the power series ∑n=0∞an(x−2)n\sum_{n=0}^{\infty} a_n (x-2)^n∑n=0∞an(x−2)n, if lim supn→∞∣an∣n=13\limsup_{n \to \infty} \sqrt[n]{|a_n|} = \frac{1}{3}limsupn→∞n∣an∣=31, what is the interval of convergence?
[0,4][0, 4][0,4]
(−1,5)(-1, 5)(−1,5)
(−1,5](-1, 5](−1,5]
[1,3][1, 3][1,3]