Answer
$\dfrac{17}{2}$
Work Step by Step
Consider two geometric series: $(5-1)+(\dfrac{5}{2} -\dfrac{1}{3})+(\dfrac{5}{4} -\dfrac{1}{9})+(\dfrac{5}{8} -\dfrac{1}{27})+...$
Here, $a=5, r=\dfrac{1}{2}$ and $a=1, r=\dfrac{1}{3}$
Formula to find the sum of a geometric series is
$S=S_1 -S_2=\dfrac{a}{1-r}-\dfrac{a}{1-r}$
or, $S=\dfrac{5}{1-\dfrac{1}{2}} -\dfrac{1}{1-\dfrac{1}{3}}$
or, $S=10 - \dfrac{3}{2}=\dfrac{17}{2}$