in my calculations i get to this solution:
\begin{aligned} H(e^{j*\omega}) & =\frac{1}{1-0.5 e^{-j\omega}} - \frac{0.5e^{-j\omega}}{1-0.5 e^{-j\omega}} &= 1\ \end{aligned}
Am i right that this is just an delta impulse?
\begin{aligned} h_2[n] & =\delta[n] \ \end{aligned}