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Homework Help: Finding a taylor series

  1. Oct 11, 2008 #1
    1. The problem statement, all variables and given/known data

    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]


    2. Relevant equations

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

    3. 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
     
  2. jcsd
  3. Oct 11, 2008 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    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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