Answer
Diverges
Work Step by Step
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$;
Let us consider $a_n=b_n=(\dfrac{1}{2})^n$
Here, $\Sigma_{n=1}^{\infty}a_n=\Sigma_{n=1}^{\infty}b_n=\Sigma_{n=1}^{\infty} (\dfrac{1}{2})^n=1$
and $\Sigma_{n=1}^{\infty}(\dfrac{a_n}{b_n})=\Sigma_{n=1}^{\infty}(1)$;
Hence, the series is divergent.