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## Homework Statement

Find the taylor series of [tex] \frac{1+z}{1-z} [/tex] where [tex] z [/tex] is a complex number and [tex] |z| < 1 [/tex]

## Homework Equations

[tex]

\sum^{\infty}_{0} z^n = \frac{1}{1-z} [/tex] if [tex] |z| < 1

[/tex]

## The Attempt at a Solution

[tex]

\sum^{\infty}_{0} z^n = \frac{1}{1-z} [/tex]

[tex] \frac{1+z}{1-z} = \sum^{\infty}_{0} z^n * (1+z) = \sum^{\infty}_{0} z^n + z^{n+1}

[/tex]

I was wondering if this is as far as you can go, or if there is a more simple closed form expression for this