Which of the Three Series Below Converges?
1) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 n - 1 } { 3 n } \right) ^ { n }$

question 256

Multiple Choice

Which of the three series below converges?
1) $\sum _ { n = 1 } ^ { \infty } \left( \frac { 2 n - 1 } { 3 n } \right) ^ { n }$
2) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 2 ^ { n } + n }$
3) $\sum _ { n = 1 } ^ { \infty } \frac { 2 ^ { n } + ( - 3 ) ^ { n } } { 3 ^ { n } }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

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Definitions:

Conscientiousness

A personality quality that embodies a person's prowess in organization, steadfastness, and a considerable sense of duty.

Agreeableness

A personality trait that involves being warm, friendly, and tactful, and having a positive outlook towards others.

Hypersensitive Narcissism

A condition characterized by extreme sensitivity to criticism and a strong need for admiration combined with a lack of empathy; closely related to vulnerable narcissism.

Entitlement

A belief that one is inherently deserving of privileges or special treatment.