Which One of the Following Series Is Divergent?
A) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 } { 3 } \right) ^ { n }$

question 134

Multiple Choice

Which one of the following series is divergent?

• A) \(\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 } { 3 } \right) ^ { n }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 2 } + 1 }\)
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n 5 ^ { n } }\)
• D) \(\sum _ { n = 2 } ^ { \infty } \frac { n } { n ^ { 2 } - 1 }\)
• E) \(\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 3 } } { n ^ { 5 } + 2 }\)
• F) \(\sum _ { n = 1 } ^ { \infty } \frac { 2 ^ { n } } { n ! }\)
• G) \(\sum _ { n = 1 } ^ { \infty } \frac { \pi } { n ^ { 2 } }\)
• H) \(\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { \pi } { n }\)

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Definitions:

Instrumental Conditioning

A form of learning in which the participant receives a reinforcer only after performing the desired response, and thereby learns a relationship between the response and the reinforcer.

Correct Responses

Correct responses refer to answers or reactions that are accurate, appropriate, or in alignment with expected outcomes in a given context.

Rewards

Benefits, recognitions, or compensations offered or received as a result of an action or behavior.

Elicited

Brought about, provoked, or drawn out by a stimulus or action; in research, responses or actions that are drawn out by specific experimental conditions.