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Finding the Maclaurin series representation

  1. Apr 15, 2013 #1
    Edit: Never mind. Got it.

    1. The problem statement, all variables and given/known data

    [tex]f(x)=\frac { x }{ { (2-x) }^{ 2 } }[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I tried finding the first derivative, the second derivative, and so on, but it just keeps getting more complicated, so I suspect I have to use binomial series.

    The issue is that binomial series needs to have the form of ##{ (1+x) }^{ k }## but I can't get it into that form. Any idea to get f(x) into that form? The x outside won't go inside the brackets.

    Here is the theorem: http://s9.postimg.org/u4qwkrmv3/Binomial_Series.png [Broken]

    Also, my textbook has only one example on binomial series and it is a simpler example.

    Attempt:

    $$f(x)=\frac { x }{ { (2-x) }^{ 2 } } \\ f(x)=\frac { x }{ 4{ (1-\frac { x }{ 2 } ) }^{ 2 } } \\ f(x)=\frac { 1 }{ 4{ x }^{ -1 }{ (1-\frac { x }{ 2 } ) }^{ 2 } }$$
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 15, 2013 #2

    LCKurtz

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    Leave the ##x/4## out in front and expand$$\left (1-\frac x 2\right)^{-2}$$then multiply the ##x/4## back in the result.

    [Edit] Apparently you got it while I was typing this.
     
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