Answer
converges to $\dfrac{1}{7}$
Work Step by Step
Formula to find the Nth partial sum of a geometric series is
$s_n=\dfrac{a(1-r^n)}{1-r}$
Formula to find the sum of a geometric series is
$S=\dfrac{a}{1-r}$
Here, $a=\dfrac{1}{8}, r=\dfrac{1}{8}$;
Thus,
$S=\dfrac{a}{1-r}=\dfrac{\dfrac{1}{8}}{1-\dfrac{1}{8}}=\dfrac{1}{7}$
Hence, the series converges to $\dfrac{1}{7}$
