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; \(\frac { 15 } { 2 }\)

---

Definitions:

Retained Earnings

The portion of net earnings not paid out as dividends, but retained by the company to be reinvested in its core business, or to pay debt.

Plant Expansion

The process of increasing the capacity or capabilities of existing facilities through additional space, equipment, or technology.

Dividend Declarations

A corporate action where a company announces the payment of dividends to its shareholders.

Retained Earnings

The portion of net earnings not paid out as dividends, but retained by the company to be reinvested in its core business or to pay debt.