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

Question

Quizplus · Accepted Answer

The series is absolutely convergent because $\frac{\arctan n}{n^4}$ is positive and decreases to 0 as $n$ approaches infinity, and $\sum \frac{1}{n^4}$ is a convergent p-series with $p > 1$.

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