Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
$$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } \arctan n } { n ^ { 4 } }$$
Select the correct answer.
A) conditionally convergent
B) absolutely convergent
C) divergent

Question

Quizplus · Accepted Answer

The series is absolutely convergent because the series of absolute values $\sum_{n=1}^{\infty} \frac{\arctan n}{n^4}$ converges by the comparison test with $\sum_{n=1}^{\infty} \frac{1}{n^4}$, which is a p-series with $p = 4 > 1$.

Determine Whether the Series Is Absolutely Convergent, Conditionally Convergent, or Divergent