If $x[n]=(0.5)^nu[n]$ and $y[n]=x[n]*x[n]$ then what is the value of $\sum\limits_{-\infty}^{\infty}y[n]$ ?
I calculated the $z-$ transform of $x[n]$ and then applied the accumulation property of $z-$transform. $$X(z) = \frac{1}{1-0.5z^{-1}}\\ Y(z) = \bigg(\frac{1}{1-0.5z^{-1}}\bigg)^2\\ \sum\limits_{n=-\infty}^{\infty}y[n] \longleftrightarrow \bigg(\frac{1}{1-0.5z^{-1}}\bigg)^2.\bigg(\frac{1}{1-z^{-1}}\bigg)$$ Please point out the mistake I am doing. Thanks in advance for the help.