Final answer:
The series converges, and its sum is -8/13. It is a geometric series with each term of the form ((-2)^n)/(11^n) and a common ratio of -2/11.
Step-by-step explanation:
The series presented is -8/11 + 64/121 - 512/1331 + 4096/14641 + … where the pattern appears to be of each term being of the form ((-2)^n)/(11^n). To evaluate whether this series converges, we can observe that it resembles a geometric series with the common ratio r = (-2/11). Since the absolute value of the common ratio is less than 1 (|r| < 1), the series converges.
A convergent geometric series has the sum S given by S = a/(1 - r), where 'a' is the first term. Here, 'a' is -8/11 and 'r' is -2/11. Substituting these values into the formula, we get S = (-8/11) / (1 - (-2/11)) = (-8/11) / (13/11), which simplifies to S = -8/13.