Provide an Appropriate Response $\mathrm { a } _ { \mathrm { n } } > 0$

question 34

Multiple Choice

Provide an appropriate response.
-Suppose that $\mathrm { a } _ { \mathrm { n } } > 0$ and $\mathrm { b } _ { \mathrm { n } } > 0$ for all $\mathrm { n } \geq \mathrm { N }$ ( $\mathrm { N }$ an integer) . If $\lim _ { \mathrm { n } \rightarrow } \frac { \mathrm { a } _ { \mathrm { n } } } { \mathrm { b } _ { \mathrm { n } } } = \infty$ , what can you conclude about the convergence of $\sum a _ { n }$ ?

• A) \(\sum a _ { n }\) converges if \(\sum b _ { n }\) converges
• B) The convergence of \(a _ { n }\) cannot be determined.
• C) \(\sum \mathrm { a } _ { \mathrm { n } }\) diverges if \(\sum \mathrm { b } _ { \mathrm { n } }\) diverges
• D) \(\sum \mathrm { a } _ { \mathrm { n } }\) diverges if \(\sum \mathrm { b } _ { \mathrm { n } }\) diverges, and \(\sum \mathrm { a } _ { \mathrm { n } }\) converges if \(\sum \mathrm { b } _ { \mathrm { n } }\) converges

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