Final answer:
The sum of the series can be found using the properties of geometric series. The series converges for all values of x such that |x| > 2.
Step-by-step explanation:
The given series can be written as:
3/14x, 28/x², 56/x³, ...
To find the sum of the series, we need to check if the series converges. For a geometric series to converge, the absolute value of the common ratio, r, must be less than 1: |r| < 1.
In this series, the common ratio is 14x / 28 = 1/2x. So, to find the values of x for which the series converges, we need to solve the inequality:
|1/2x| < 1
Simplifying the inequality, we have:
1/2|x| < 1
|x| > 2
Therefore, the series converges for all values of x such that |x| > 2.