## Thomas' Calculus 13th Edition

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.