∑_{n=−∞}^{∞} x[n]z^{−n} = ∑_{n=0}^{∞} 0.5^{n}z^{−n} = ∑_{n=0}^{∞} (\frac{0.5}{z})^{n} = \frac{1}{1 − 0.5z^{−1}}