1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Power Series
  1. Power series (Replies: 5)

  2. Power series (Replies: 3)

  3. Power Series (Replies: 13)

  4. Power series (Replies: 11)

  5. Power Series (Replies: 2)

Loading...