Provide an Appropriate Response $\left\{ a _ { n } \right\}$

question 259

Multiple Choice

Provide an appropriate response.
-Which of the following statements is false?

• A) The sequences \(\left\{ a _ { n } \right\}\) and \(\left\{ b _ { n } \right\}\) must be positive for all \(n\) to apply the Limit Comparison Test.
• B) All of these are true.
• C) If \(\left\{ a _ { n } \right\}\) and \(\left\{ b _ { n } \right\}\) meet the conditions of the Limit Comparison test, then, if \(\lim _ { n \rightarrow } \frac { a _ { n } } { b _ { n } } = 0\) and \(\sum b _ { n }\) converges, then \(\sum a _ { n }\) converges.
• D) The series \(\sum a _ { n }\) must have no negative terms in order for the Direct Comparison test to be applicable.

---

Definitions:

Heuristics

Mental shortcuts or rules of thumb that ease the cognitive load of making a decision.

Decision Making

The process of identifying and choosing alternatives based on the values and preferences of the decision-maker.

Shelf-space

The amount of area or space available on shelves in a store allocated to display products.

Cereals Marketers

Professionals involved in promoting and selling grains such as wheat, maize, oats, and barley.