1. The problem asks for the sum of the infinite geometric series: $$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots$$ 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. Here, the first term $a = 1$ and the common ratio $r = \frac{1}{2}$. 4. Since $|r| = \frac{1}{2} < 1$, the sum converges. 5. Substitute the values into the formula: $$S = \frac{1}{1 - \frac{1}{2}} = \frac{1}{\frac{1}{2}} = 2$$ 6. Therefore, the sum of the infinite geometric series is $2$. Final answer: 2