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

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