Identify the Interval of Convergence of a Power Series $\sum _ { n = 1 } ^ { \infty } ( - 3 ) ^ { n } n x ^ { n - 1 }$

question 6

Multiple Choice

Identify the interval of convergence of a power series
$\sum _ { n = 1 } ^ { \infty } ( - 3 ) ^ { n } n x ^ { n - 1 }$

• A) \(- 3 < x < 3\)
• B) \(- 1 < x < 1\)
• C) \(- \frac { 1 } { 3 } < x < \frac { 1 } { 3 }\)
• D) \(0 < x < 3\)
• E) \(- \frac { 1 } { 6 } < x < \frac { 1 } { 6 }\)

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Definitions:

Cross-sectional

A research design that collects data from different participants at a single point in time to compare across groups or variables.

Research Design

The framework or strategy for a study that guides the collection and analysis of data to address research questions effectively.

Tested

The process of evaluating skills, performance, reliability, or quality by administering a series of questions or activities under controlled conditions.

Equivalent Samples

Groups in a study or experiment that are made as similar as possible to ensure that results are due to the variable being tested rather than pre-existing differences among participants.