Provide an Appropriate Response $\frac { 1 } { 1 + x }$

question 38

Multiple Choice

Provide an appropriate response.
-Derive the series for $\frac { 1 } { 1 + x }$ for $x > 1$ by first writing $\frac { 1 } { 1 + x } = \frac { 1 } { x } \frac { 1 } { 1 + 1 / x }$ .

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { x ^ { n } }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { x ^ { n } }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { x ^ { n + 1 } }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { x ^ { n + 1 } }\)

---

Definitions:

Compassionate

Showing sympathy and concern for the sufferings or misfortunes of others.

Autokinetic Phenomenon

A visual illusion where a stationary point of light in a dark room appears to move due to small involuntary eye movements.

Social Norms

Informal understandings that govern the behavior of members of a society.

Sherif

An influential social psychologist known for his work on understanding group conflicts, social norms, and conformity through the Robbers Cave experiment.