Answer
See below.
Work Step by Step
Consider $a_n=(\dfrac{1}{4})^n; b_n=(\dfrac{1}{2})^n$
Let $A=\Sigma_{n=1}^{\infty}a_n=\dfrac{1}{3}$ and $B=\Sigma_{n=1}^{\infty}b_n=1$
and $\Sigma_{n=1}^{\infty}(\dfrac{a_n}{b_n})=\Sigma_{n=1}^{\infty}(\dfrac{1}{2})^n=1 \ne \frac{A}{B}$
