Determine If the Series Converges Absolutely, Converges, or Diverges $$\sum _ { n = 1 } ^ { \infty } ( \cos n \pi ) \left( \frac { n ! } { 7 ^ { n } } \right)$$

question 359

Multiple Choice

Determine if the series converges absolutely, converges, or diverges.
- $$\sum _ { n = 1 } ^ { \infty } ( \cos n \pi ) \left( \frac { n ! } { 7 ^ { n } } \right)$$

• A) converges conditionally
• B) diverges
• C) converges absolutely

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Definitions:

Nietzsche

Friedrich Nietzsche was a German philosopher, cultural critic, composer, poet, and philologist, known for his critique of morality, religion, and contemporary culture, promoting the concept of the "Übermensch."

Chaos

A state of extreme confusion and disorder, often used to describe a lack of order or predictability in a system.

Aesthetic Judgment

The process or act of analyzing and evaluating the beauty, artistry, or taste of something, often influenced by personal preferences, cultural norms, and societal trends.

Kant

A German philosopher of the 18th century, Immanual Kant is regarded as a central figure of modern philosophy who argued that reason is the source of morality and that aesthetics arises from a faculty of disinterested judgment.