Find the Sum of the Series $\sum _ { n = 2 } ^ { \infty } ( n - 1 ) x ^ { n }$

question 52

Essay

Find the sum of the series $\sum _ { n = 2 } ^ { \infty } ( n - 1 ) x ^ { n }$ , where $| x | < 1$ .

---

Definitions:

Social Class

A division of a society based on social and economic status, influencing one's opportunities, lifestyle, and attitudes.

Leisure Interests

Activities or hobbies pursued for enjoyment, relaxation, or pleasure during free time.

Exogamy

A cultural practice that requires marrying outside one’s group (often used interchangeably with heterogamy).

Emotionally Committed

describes individuals who invest significant emotional energy into relationships, projects, or goals, often leading to strong loyalty and dedication.