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

question 290

Multiple Choice

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

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

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Definitions:

Generalization

A broad statement or an idea that applies to a group of items or situations, often derived from specific instances.

Instances

Specific examples or occurrences of a particular event or situation.

African Languages

The languages native to the African continent, which comprise several language families and thousands of languages and dialects.

Disconfirming Instances

Observations or examples that contradict the predictions or implications of a hypothesis or theory.