#### Answer

First four terms: $0.3, 0.03, 0.003, 0.0003$
Sum: $S_\infty = \frac{1}{3}$.

#### Work Step by Step

The next term is the previous term multiplied by a factor of $0.1$.
The infinite series is a geometric series, with a common ratio $r$ of $0.1$, which is less than $1$. Given an initial term of $a_0$ and common ratio $r$, we can find the sum by $S_\infty = \frac{a_0}{1-r}$.
$S_\infty = \frac{0.3}{1-0.1} = \frac{1}{3}$.