# How do you find the sum of the infinite geometric series Sigma (0.4)^n from n=0 to oo?

$\frac{5}{3}$
Where $\left\mid r \right\mid < 1$, note that ${\sum}_{n = 0}^{\infty} {r}^{n} = \frac{1}{1 - r}$.
Here, since $\left\mid 0.4 \right\mid < 1$, we see that
${\sum}_{n = 0}^{\infty} {\left(0.4\right)}^{n} = \frac{1}{1 - 0.4} = \frac{1}{0.6} = \frac{1}{3 / 5} = \frac{5}{3}$