Consider the following series. Answer the following questions. 1. Find the values of \( x \) for which the series converges. Answer (in interval notation): 2. Find the sum of the series for those values of \( x \). Write the formula in terms of \( x \) Sum:

To determine the values of \( x \) for which the series converges, we first identify what type of series we are dealing with (for simplicity, let’s assume it’s a power series). For a power series \( \sum a_n(x - c)^n \), convergence typically depends on the radius of convergence \( R \). The series converges for \( |x - c| < R \). 1. The series converges for \( x \) in the interval \( (c - R, c + R) \). 2. If the series converges to a specific form, say \( \sum a_n (x - c)^n \), the closed-form expression can often be simplified into a function. For example, the sum might resemble \( S(x) = \frac{1}{1 - (x - c)} \) for a geometric series. Thus, the sum for those values of \( x \) would be given by the formula \( S(x) = f(x) \) for your specific series.