Which of the Following Series Are Convergent, but Not Absolutely $\sum _ { n = 1 } ^ { \infty } ( - e ) ^ { - n }$

question 143

Multiple Choice

Which of the following series are convergent, but not absolutely convergent?
1) $\sum _ { n = 1 } ^ { \infty } ( - e ) ^ { - n }$
2) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { - n } n ^ { - 1 }$
3) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { - n } n ^ { - 2 }$

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

---

Definitions:

Driven

Being highly motivated or determined to achieve certain goals or outcomes.

School

An institution for educating children and young people in various subjects, developing skills and knowledge for personal growth and future employment.

Observational Learning

A learning process where individuals change their behaviors by observing and imitating the actions of others.

Rat Maze

An experimental setup used in behavioral studies, often to assess learning, memory, and problem-solving abilities in rodents.