For the power series ∑n=0∞(x−2)n3n\sum_{n=0}^{\infty} \frac{(x-2)^n}{3^n}∑n=0∞3n(x−2)n, what is the interval of convergence?
∣x−2∣<3|x-2| < 3∣x−2∣<3, i.e., −1<x<5-1 < x < 5−1<x<5
∣x−2∣<1|x-2| < 1∣x−2∣<1, i.e., 1<x<31 < x < 31<x<3
∣x∣<3|x| < 3∣x∣<3, i.e., −3<x<3-3 < x < 3−3<x<3
∣x−2∣≤3|x-2| \leq 3∣x−2∣≤3, i.e., −1≤x≤5-1 \leq x \leq 5−1≤x≤5