- #1
adjklx
- 13
- 0
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