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.

Question

Quizplus · Accepted Answer

The Limit Comparison Test does not require the sequences $\left\{ a _ { n } \right\}$ and $\left\{ b _ { n } \right\}$ to be positive for all $n$; it only requires that the sequences be positive for all $n$ beyond some initial point $N$.

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

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