This source states that the unit step function in the Z-domain is \$\frac{z}{z-1}\$. However, in its derivation it states \$\sum_{k=0}^{\infty} z^{-k} = \frac{z}{z-1}\$.
But doesn't that last relation only hold true for \$z>1\$? I don't see how that condition is met. I know that the poles have to be in the unit circle for the system to be stable, but I don't see if and how that connects to the condition above.
What am I missing?