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Adding geometric series

  1. Nov 28, 2004 #1
    Find a power series for the function centered at c and determine the interval of convergence.
    c = 0


    After some partial fractions work and getting the partials in the form of


    I have

    [tex]\sum x^n + \sum(-x)^n[/tex]

    if I factor out the x^n's I get


    This is where I'm stuck, the solution manual shows it then going to


    I've been staring at this thing for 15 mins and can't see how it's possible. Could someone give me a little push in the right direction with this? Thanks.
  2. jcsd
  3. Nov 28, 2004 #2

    Dr Transport

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    Science Advisor
    Gold Member

    write out th efirst few terms and you will see the answer, n = 0, 1+1 = 2; n = 1, (1 + (-1))x = 0, etc...,
  4. Nov 28, 2004 #3

    n has to be even so that the coefficient wouldn't be zero. Then you have 1+1 = 2 and the exponent is written as 2n to make sure it is even...

  5. Nov 28, 2004 #4
    Thanks guys, I wish the book or the manual would make it a little clearer when they do stuff like this. The way it's written seems to imply that there's some algebra going on to get to the final result.
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