Find the Values of X for Which the Geometric Series $$\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( 4 \mathrm { x } ) ^ { 2 \mathrm { n } }$$

question 138

Multiple Choice

Find the values of x for which the geometric series converges.
- $$\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( 4 \mathrm { x } ) ^ { 2 \mathrm { n } }$$

• A) \(| x | < 1\)
• B) \(| x | < 4\)
• C) \(| x | < \frac { 1 } { 4 }\)
• D) \(| x | < 8\)

---

Definitions:

Virtue Ethics

Virtue ethics focuses on the moral character of an individual as the key element of ethical thinking, rather than rules about the acts themselves or their consequences.

Consequences

The results or outcomes that naturally follow from a specific action or set of conditions, often used in the context of cause-and-effect relationships.

Actions

Steps or measures taken to achieve a goal, execute a plan, or respond to events.

Code Of Ethics

A set of principles designed to guide the conduct of members within an organization, ensuring professional behavior and decision-making.