Answer
$\dfrac{5}{3}$
Work Step by Step
The sum of a geometric series can be found as:
$S_n=\dfrac{a_1}{1-r}$
where, $a_1$ denotes the first term and the $r$ is common ratio.
We are given that $\Sigma_{n=0}^{\infty} (\dfrac{2}{5})^n$
This can be further written as: $\Sigma_{n=0}^{\infty} (\dfrac{2}{5})^n=1+\dfrac{2}{5}+(\dfrac{2}{5})^2+(\dfrac{2}{5})^3+.......$
So, we have $a_1=1$ and $r=\dfrac{2}{5}$
Thus, the sum of a geometric series is:
$S_n=\dfrac{1}{1-\dfrac{2}{5}}=\dfrac{5}{3}$
