How to compute $ \sum_{k=0}^\infty \frac{4^k}{z^k} $

Question

I need to compute: $$ \sum_{k=0}^\infty \frac{4^k}{z^k} $$

Can someone help me?

Answer 1

Hint: $$\sum_{k=0}^{+\infty} r^k=\frac{1}{1-r},\quad |r|<1.$$ Here $r=\dfrac{4}{z}$ for appropriate $z$.

Answer 2

Let $r=\dfrac 4 z$, and $s$ be the sum. Then $r s = s-1$ and so $s = \dfrac 1 {1-r}$.