For which set of values does the power series ∑n=1∞(x−1)nn2\sum_{n=1}^{\infty} \frac{(x-1)^n}{n^2}∑n=1∞n2(x−1)n converge?
∣x−1∣<1|x-1| < 1∣x−1∣<1 (open interval (0,2)(0, 2)(0,2))
0≤x≤20 \leq x \leq 20≤x≤2 (closed interval [0,2][0,2][0,2])
0<x<20 < x < 20<x<2 (open interval (0,2)(0,2)(0,2))
1≤x≤31 \leq x \leq 31≤x≤3 (closed interval [1,3][1,3][1,3])