1. The problem is to simplify the expression $$\frac{1-\left(\frac{1}{2}\right)^n}{1-\frac{1}{2}}$$. 2. First, simplify the denominator: $$1-\frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}$$. 3. Substitute this back into the expression: $$\frac{1-\left(\frac{1}{2}\right)^n}{\frac{1}{2}}$$. 4. Dividing by \(\frac{1}{2}\) is equivalent to multiplying by 2: $$2 \times \left[1-\left(\frac{1}{2}\right)^n\right] = 2 - 2 \times \left(\frac{1}{2}\right)^n$$. 5. Simplify the multiplication inside: $$2 - 2 \times \frac{1}{2^n} = 2 - \frac{2}{2^n} = 2 - \frac{1}{2^{n-1}}$$. Thus, the simplified form of the given expression is: $$2 - \frac{1}{2^{n-1}}$$.