S = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots This is an infinite geometric series with: • First term: a = 1 • Common ratio: r = \frac{1}{2} The sum of an infinite geometric series is given by the formula: S = \frac{a}{1 - r} Substituting the values: S = \frac{1}{1 - \frac{1}{2}} = \frac{1}{\frac{1}{2}} = 2 Thus, the sum of the series is: \mathbf{2}