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 Representation of (1+x)/(1-x)

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data

    For the power series representation of, f(x)=1+x1−x which is 1+2∑from n=1 to inf (x^n), Where does the added 1 in front come from? How do I get to this answer from ∑n=0 to inf (x^n)+∑n=0 to inf (x^(n+1))

    2. Relevant equations



    3. The attempt at a solution

    I arrived at ∑n=0 to inf x^n + ∑ n=0 to inf x^(n+1)
     
  2. jcsd
  3. Apr 16, 2013 #2
    The 1 in front comes from using long division to isolate the 1/(1-x) term. I'm not sure what you're asking in your second question though. If you want to change the index of a summation, you can do it entirely artificially. Namely, if you want [itex] \sum_{n=1}^\infty x^n [/itex] to look like a sum where the lower index starts at 0 instead of 1, define a new index k = n-1.
     
  4. Apr 17, 2013 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    ##x^0=1##
     
  5. Apr 17, 2013 #4
    Rereading your question, I now understand what you are saying. Have you been doing as suggested? Use long division to break up the rational function, then use vela's comment about how [itex] x^0 = 1 [/itex] and you'll get the answer your originally posted.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Power Series Representation of (1+x)/(1-x)
Loading...