Final answer:
The student's question about the convergence or divergence of a geometric series and its sum requires clarification due to typos. Typically, a geometric series converges if the absolute value of the common ratio is less than 1, and its sum can be calculated using a specific formula.
Step-by-step explanation:
To determine whether the geometric series is convergent or divergent, and if it is convergent, to find its sum, we must first identify the first term (a) and the common ratio (r) of the series. However, the given information appears to contain typos or errors as the series is not presented in a discernible format. A geometric series takes the form a, ar, ar2, ..., where a is the first term and r is the ratio between successive terms. The sum of an infinite geometric series can be found using the formula S = a / (1 - r) if |r| < 1, indicating convergence. If |r| ≥ 1, the series is divergent and does not have a finite sum.