Answer
Diverges
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
Consider $a_n=b_n=(\dfrac{1}{2})^n$
The given series $\Sigma_{n=1}^{\infty}a_n=\Sigma_{n=1}^{\infty}b_n=\Sigma_{n=1}^{\infty} (\dfrac{1}{2})^n=1$
and $\Sigma_{n=1}^{\infty}(\dfrac{a_n}{b_n})=\Sigma_{n=1}^{\infty}(1)$, which diverges.
