How many terms of the series do we need to add in order to find the sum to the indicated accuracy? Select the correct answer.
$$\sum _ { n = 1 } ^ { \infty } 2 \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 2 } } ( \text { |error } \mid )

Question

How many terms of the series do we need to add in order to find the sum to the indicated accuracy? Select the correct answer.
$$\sum _ { n = 1 } ^ { \infty } 2 \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 2 } } ( \text { |error } \mid ) < 0.0798$$
A) $n = 6$
B) $n = 5$
C) $n = 12$
D) $n = 8$
E) $n = 13$

Quizplus · Accepted Answer

The series is an alternating series, and the error is less than the absolute value of the first omitted term. For $n = 6$, the next term is $\left|2 \frac{(-1)^{7}}{7^2}\right| = \frac{2}{49} \approx 0.0408$, which is less than 0.0798.

How Many Terms of the Series Do We Need to Add