Determine If the Series Converges or Diverges $$\sum _ { n = 1 } ^ { \infty } \frac { 9 n } { ( 2 n - 1 ) ^ { 2 } ( 2 n + 1 ) ^ { 2 } }$$

question 78

Multiple Choice

Determine if the series converges or diverges. If the series converges, find its sum.
- $$\sum _ { n = 1 } ^ { \infty } \frac { 9 n } { ( 2 n - 1 ) ^ { 2 } ( 2 n + 1 ) ^ { 2 } }$$

• A) converges; \(\frac { 27 } { 8 }\)
• B) converges; \(\frac { 21 } { 2 }\)
• C) converges; \(\frac { 9 } { 8 }\)
• D) converges; \(\frac { 15 } { 2 }\)

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Definitions:

Analyzability

refers to the extent to which problems or tasks can be broken down into smaller, manageable components, making them easier to understand, analyze, and solve.

Network Structures

The arrangement and interconnection of elements in a system, often referring to how people or positions are interconnected within organizations.

Core Organization

The fundamental, central part of an organization that is essential for its operation and defines its main purpose.

Matrix Structure

An organizational framework that combines two or more types of organizational structures, typically functional and product-based divisions, to leverage the benefits of both.