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

question 169

Multiple Choice

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

• A) \(0 < x \leq 2\)
• B) \(- 2 \leq x < 0\)
• C) \(- 2 < x \leq 0\)
• D) \(0 \leq x < 2\)
• E) \(- 2 < x < 0\)
• F) \(0 < x < 2\)
• G) \(0 \leq x \leq 2\)
• H) \(- 2 \leq x \leq 0\)

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Definitions:

Applied Voltage

The voltage that is applied across a component or circuit, initiating the flow of current.

Inductive VARs

In power systems, inductive VARs (Volt-Ampere Reactive) are reactive power components generated by inductive loads, contributing to the overall power factor but not to the actual work performed.

Power Factor

A dimensionless measure of how effectively electrical power is converted into useful work output, particularly the ratio of real power to apparent power in a circuit.

Capacitive VARs

Reactive power measured in Volt-Ampere Reactive (VAR) generated by capacitive loads, which can be used for power factor correction in electrical systems.