Provide an Appropriate Response $\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( \mathrm { x } - 5 ) ^ { \mathrm { n } }$

question 107

Multiple Choice

Provide an appropriate response.
-If the series $\sum _ { \mathrm { n } = 0 } ^ { \infty } ( - 1 ) ^ { \mathrm { n } } ( \mathrm { x } - 5 ) ^ { \mathrm { n } }$ is integrated term by term, for what value(s) of $\mathrm { x }$ does the new series converge?

• A) \(4 \leq x < 6\)
• B) \(4 < x \leq 6\)
• C) \(4 < x < 6\)
• D) \(4 \leq x \leq 6\)

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Definitions:

Facial Feedback Effect

The theory that facial expressions can influence emotional experiences, suggesting that smiling can make one feel happier.

Physiological Responses

automatic reactions of the body to internal or external stimuli, such as changes in heart rate, hormone levels, and muscle tension.

Expressing Emotion

The action of conveying feelings or emotions through words, gestures, facial expressions, or other behaviors.

Facial Expressions

The movements or positions of the face that convey a person's emotions, intentions, or social signals.