$\displaystyle \sum_{n=0}^\infty \frac{2^{n}}{5^{2n+1}}$

I broke it up like $\displaystyle {\frac{1}{5}}\sum_{n=0}^\infty ({\frac{2}{25}})^{n}$

I calculated the sum $\displaystyle S = \frac{1}{5}[\frac{\frac{1}{5}}{\frac{25}{25}-\frac{2}{25}}] $

Which ends up being $\displaystyle S = \frac{1}{23}$ ?