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

question 24

Multiple Choice

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

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Definitions:

Shyness

a personality characteristic that involves feeling apprehensive or inhibited in social situations, often leading to avoidance or discomfort around others.

Extraversion

A personality trait typified by sociability, talkativeness, assertiveness, and high levels of emotional expressiveness.

Self-Concept

An individual's understanding of themselves, encompassing self-awareness, self-esteem, and the self-image.

Self-Esteem

A feeling of personal worth and ability that is fundamental to an individual's identity.