Final answer:
The maximum possible error of using the first 6 terms to approximate the sum of the series can be found by comparing the sum of the first 6 terms to the sum of the entire series. The error is less than or equal to the absolute value of the next term omitted.
Step-by-step explanation:
The maximum possible error of using the first 6 terms to approximate the sum of the series ∑_{n=1}^{\infty} \left((-1)^{n+1}\right) / n^2 can be found by comparing the sum of the first 6 terms to the sum of the entire series. The series is an alternating series with decreasing terms, so the error is less than or equal to the absolute value of the next term omitted, which is 1 / 49. Therefore, the maximum possible error is 1 / 49, which is less than both option (A) 1/16 and option (B) 1/25.