#### Answer

First four terms: $0.6, 0.06, 0.006, 0.0006$
Sum: $S_\infty = \frac{2}{3}$

#### Work Step by Step

Each subsequent term is the previous term multiplied by a factor of $0.1$.
$a_1 = 0.6$
$a_2 = 0.06$
$a_3 = 0.006$
$a_4 = 0.0006$
The infinite series is a geometric sequence with a common ratio of $r = 0.1$, which is less than $1$. Given the first term of a series, $a_1$, and a common ratio $r$ that's less than $1$, the sum is given by $Sum: S_\infty = \frac{a_1}{1-r}$
Sum: $S_\infty = \frac{0.6}{1-0.1} = \frac{2}{3}$