1. The problem is to find the sum of the infinite geometric series given by the sequence. 2. The formula for the sum $S$ of an infinite geometric series with first term $a$ and common ratio $r$ (where $|r|<1$) is: $$S = \frac{a}{1-r}$$ 3. Identify the first term $a$ and the common ratio $r$ from the sequence. 4. Verify that the absolute value of the common ratio $|r|$ is less than 1 to ensure convergence. 5. Substitute the values of $a$ and $r$ into the formula and simplify to find the sum. 6. If any factors cancel during simplification, show the cancellation using $\cancel{\cdot}$ notation. 7. The final answer is the sum $S$ of the infinite series.