Answer
$\dfrac{10}{3}$
Work Step by Step
Given: $2+\dfrac{4}{5}+\dfrac{8}{25}+\dfrac{16}{25}+...$
The series can be re-written as: $2(1+\dfrac{2}{5}+\dfrac{4}{25}+\dfrac{8}{25}+...)$
or, $2(1+\dfrac{2}{5}+(\dfrac{2}{5})^2+(\dfrac{2}{5})^3+...)$
Here, $a=1, r=\dfrac{2}{5}$
Formula to find the sum of a geometric series is
$S=\dfrac{a}{1-r}$
Thus, $S=2(\dfrac{1}{1-\dfrac{2}{5}})=\dfrac{10}{3}$
