Answer
$\frac{2}{3}$
Work Step by Step
$\frac{2}{5} + \frac{4}{25} + \frac{8}{125} +\frac{16}{625} + \frac{32}{3125} + ... = \sum_{n = 1}^{\infty}(\frac{2}{5})^n$
The series is geometric with a = $\frac{2}{5}$ and ratio r = $\frac{2}{5}$. Since |r| = $\frac{2}{5}$ < 1, it converges to $\frac{\frac{2}{5}}{1 - \frac{2}{5}}$ = $\frac{2}{3}$
