Answer
$\dfrac{1}{12}$
Work Step by Step
Formula to calculate the Nth partial sum of a geometric series is
$s_n=\dfrac{a(1-r^n)}{1-r}$
Formula to calculate the Sum of a geometric series is:
$S=\dfrac{a}{1-r}$
Here, $a=\dfrac{1}{16}, r=\dfrac{1}{4}$
Thus, $S=\dfrac{a}{1-r}=\dfrac{\dfrac{1}{16}}{1-\dfrac{1}{4}}$
or, $S=\dfrac{\dfrac{1}{16}}{\dfrac{3}{4}}=\dfrac{1}{12}$
