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

question 9

Essay

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

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Definitions:

Price-Fixing

An illegal agreement among competitors to set prices at a certain level, rather than letting them be determined naturally by supply and demand.

Economic Efficiency

A state in which resources are allocated in a way that maximizes the production of goods and services at the lowest cost, while achieving the highest possible welfare or utility.

Negative Externalities

Costs experienced by third parties due to the actions of others that are not reflected in market prices.

Clayton Act

A U.S. antitrust law, adopted in 1914, aimed at protecting competition by prohibiting certain actions that lead to anticompetitiveness.