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

Question

Quizplus · Accepted Answer

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

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