Answer
$\dfrac{23}{2}$
Work Step by Step
We have 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 $a=1, r=\dfrac{1}{3}$
The sum of a geometric series can be found as:
$S=s_1+s_2=\dfrac{a}{1-r}$
or, $=\dfrac{5}{1-\dfrac{1}{2}}+\dfrac{1}{1-\dfrac{1}{3}}=10+\dfrac{3}{2}=\dfrac{23}{2}$
