Final answer:
The series converges when x belongs to the closed interval [-1,1].
Step-by-step explanation:
To determine the values of x for which the series converges, we need to consider the limit of the absolute values of each term. The series is given by (-9)^n * x^n for n = 1. We want the absolute value of each term to approach zero as n approaches infinity for the series to converge. Since (-9)^n is always positive and x^n is either positive or negative, we need the absolute value of x^n to be less than or equal to 1.
When x^n = 1, x = 1. When x^n = -1, x = -1. Therefore, the series converges when x belongs to the closed interval [-1,1]. This can be expressed in interval notation as [-1,1].