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Homework Help: Power Series

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the power series representation for the function f(x)=x/(x^2-3x+2) and determine the interval of convergence.


    2. Relevant equations



    3. The attempt at a solution
    First I separate into partial fractions 2/(x-2) - 1/(x-1)

    2/(x-2) = sum n=0 to infinity (x/2)^n
    1/(x-1) = sum n=0 to infinity (x)^n

    Now I just dont know how to make them one power series representation.
     
  2. jcsd
  3. Sep 28, 2011 #2

    dynamicsolo

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    Homework Helper

    Temporarily, let x = 2u and add the two power series together. You will need to find the pattern of the coefficients for the general term. You can always switch back to using x as a variable at the end. (There may be something more clever to use, but I'm juggling something else just now...)

    Watch out, by the way: 1 + x + x2 + ... is 1/(1 - x) .

    EDIT: thought about this a bit more -- the cleaner way to do this is to write the [itex](\frac{x}{2})^{n}[/itex] terms as [itex]\frac{x^{n}}{2^{n}}[/itex] . You will still have a little work on sorting out the general term for the single series representation.
     
    Last edited: Sep 28, 2011
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