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Why same initial value in power series

  1. May 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Find a power series representation for the function below & determine the radius of convergence.

    f (x)=(1+x)/(1-x)2

    2.Relevant equation

    Shown in attached image below which is the solution the problem.

    3.The attempt at a solution

    pff.png
    I'm trying to fathom the solution here.

    I am pretty sure the initial value is the value of n. If so, it does not seem that the starting values were made equal here. Unless it has something to do with the 1+ ∑ that shows up on the fourth line?

    Please help
     
  2. jcsd
  3. May 29, 2015 #2

    Mark44

    Staff: Mentor

    The starting values are not equal in the third line. The comment to this effect is not that the starting values were made equal, but rather that this is the goal, which happens in the 4th line.

    Note that ##\sum_{n = 0}^{\infty} (n + 1)x^n = 1x^0 + \sum_{n = 1}^{\infty} (n + 1)x^n = 1 + \sum_{n = 1}^{\infty} (n + 1)x^n##. Is that what you're asking about?
     
  4. May 29, 2015 #3
    Thanks for your quick response. I fathom now.
     
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