Finding a taylor series

  • Thread starter adjklx
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
7
Divide the sum into two parts and notice that

[tex]\sum_{n=0}^{\infty} z^{n+1}=\left( \sum_{n=0}^{\infty} z^{n} \right) - 1[/tex]
 

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