For What Values of X Does the Series Converge Absolutely $$\sum _ { n = 0 } ^ { \infty } ( 3 x ) ^ { n }$$

question 291

Multiple Choice

For what values of x does the series converge absolutely?
- $$\sum _ { n = 0 } ^ { \infty } ( 3 x ) ^ { n }$$

• A) \(x > \frac { 1 } { 3 }\)
• B) \(- \frac { 1 } { 3 } < x < \frac { 1 } { 3 }\)
• C) \(0 < x < \frac { 1 } { 3 }\)
• D) None

---

Definitions:

Axons

Long, threadlike parts of nerve cells along which impulses are conducted from the cell body to other cells.

Propagating Action Potential

The process by which an electrical impulse travels along the length of a neuron, enabling communication within the nervous system.

Myelin

A fatty substance that surrounds and insulates nerve fibers, increasing the speed at which electrical impulses are conducted.

Conduction Speed

The rate at which an electrical impulse travels along a nerve or muscle fiber.