### Home > PC3 > Chapter 12 > Lesson 12.1.3 > Problem12-43

12-43.

You know that $0.33333... = \frac { 1 } { 3 }$. Here is a short proof to help justify the fact.

1. Write $0.333…$. as an infinite geometric series.

Represent each digit separately.

2. What are the initial term and common ratio?

3. Write and simplify an expression for the sum of the infinite geometric series.

$S = \frac{a}{1-r}$