Which of the following is true for the infinite series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 8 n ^ { 2 } } ?$
A)Its sequence of partial sums is not bounded from above.
B)Its sequence of partial sums is decreasing.
C)It is absolutely convergent.
D)It is conditionally convergent.
E)It is divergent.

Question

Quizplus · Accepted Answer

The series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 8 n ^ { 2 } }$ is absolutely convergent because the series formed by taking the absolute values of its terms, $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 8 n ^ { 2 } }$, is a convergent p-series with $p = 2 > 1$.

Which of the Following Is True for the Infinite Series ∑n=1∞(−1)n8n2?\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 8 n ^ { 2 } } ?∑n=1∞​8n2(−1)n​?

Which of the Following Is True for the Infinite Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 8 n ^ { 2 } } ?$