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Sum of Geometric Series

  1. Nov 29, 2008 #1
    1. Sum the Geometric Series 1-x+x2-x3+x4

    and hence simplify the function

    [f(x)]4 = 1 - x5
    1-x+x2-x3+x4

    2. Relevant equations



    3. Not sure I quite get understand this properly, as my attempt doesnt seem quite right.


    Basically Ive gotten

    S=1-x+x2-x3+x4

    S=1-1+x-x2+x3
    x x

    which then subtracted becomes

    s(1 - 1) = (1-1)+2x+x+x
    x x

    = 1 +4x
    x

    Then, putting that into the simplifying function part gives me

    f(x) =

    1 -x5
    -1 +4x
    x
     
    Last edited: Nov 29, 2008
  2. jcsd
  3. Nov 29, 2008 #2
    Notice that

    [tex]1-x+x^2-x^3+\ldots=\sum_{n=0}^{\infty}(-1)^nx^n=\sum_{n=0}^{\infty}(-x)^n[/tex]
     
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