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. Rewrite the original expression using this: $$\frac{1-\left(\frac{1}{2}\right)^n}{\frac{1}{2}}$$. 4. Dividing by $$\frac{1}{2}$$ is equivalent to multiplying by 2, so: $$2 \left(1-\left(\frac{1}{2}\right)^n\right)$$. 5. Distribute the 2: $$2 - 2\left(\frac{1}{2}\right)^n$$. 6. Rewrite $$2\left(\frac{1}{2}\right)^n$$ as: $$2 \cdot \frac{1}{2^n} = \frac{2}{2^n} = 2^{1-n}$$. 7. Therefore, the simplified expression is: $$2 - 2^{1-n}$$. Thus, the simplified form of the given expression is $$2 - 2^{1-n}$$.