real analysis - Calculate the limit of $sum_{k=0}^{infty}(-1)^kz^k, z in (0,1)$

How can I calculate the limit of $\sum_{k=0}^{\infty}(-1)^kz^k, z \in (0,1)$? I only know how to show whether a given sequence converges, but I'm not sure how to apply the theorems about infinite series to calculate limits. Can anybody help please?

Answer

Write $(-1)^kz^k = (-z)^k$, then $S = \dfrac{1}{1- (-z)} = \dfrac{1}{1+z}$ because it is a geometric series with $|-z| = z < 1$