1. **State the problem:** Find the sum of the infinite geometric series $$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$$. 2. **Identify the first term and common ratio:** The first term $$a = 1$$. The common ratio $$r = \frac{1}{2}$$ because each term is half the previous term. 3. **Check if the series converges:** Since $$|r| = \frac{1}{2} < 1$$, the infinite geometric series converges. 4. **Use the formula for the sum of an infinite geometric series:** $$S = \frac{a}{1 - r}$$ 5. **Substitute the values:** $$S = \frac{1}{1 - \frac{1}{2}} = \frac{1}{\frac{1}{2}} = 2$$ 6. **Conclusion:** The sum of the infinite geometric series is $$2$$. **Final answer:** 2