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:

Expected Value

The anticipated value or average outcome of a random variable, taking into account all possible outcomes weighted by their probabilities.

Probabilities

A measure expressing the likelihood of occurrence of a given event, typically defined on a scale from 0 to 1, where 0 means the event cannot occur and 1 indicates certainty.

Expected Value

A statistical concept that calculates the weighted average of all possible values for a random variable.

Probabilities

A numerical assessment ranging from 0 to 1 that quantifies how likely an event is to take place.