Find the Series' Radius of Convergence $$\sum _ { n = 0 } ^ { \infty } \frac { ( x - 1 ) ^ { n } } { 2 n + 5 }$$

question 23

Multiple Choice

Find the series' radius of convergence.
- $$\sum _ { n = 0 } ^ { \infty } \frac { ( x - 1 ) ^ { n } } { 2 n + 5 }$$

• A) 2
• B) 0
• C) \(\infty\), for all \(x\)
• D) 1

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Definitions:

Marx

Refers to Karl Marx, a 19th-century philosopher and economist known for his ideas about capitalism and communism.

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Harriet Martineau, a British social theorist and Whig writer, often considered the first female sociologist for her significant contributions to the field.

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The study of society focused on understanding the dynamics of social class and the complexities of socio-economic stratification.

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A method whereby the sociologist becomes both a participant in the group being studied and a scientific observer of the group.