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Sum of a geometric series

  1. Apr 23, 2006 #1
    Hi

    Can I claim that in order to find the sum of the series:

    [tex]\sum_{n = 0} ^{\infty} 2^{- n}[/tex]

    [tex]\sum_{n = 0} ^{\infty} 2^{- n} = \sum_{n = 0} ^{\infty} x^n = \frac{1}{1-x} [/tex] ???


    Sincerely Yours
    Fred
     
    Last edited: Apr 23, 2006
  2. jcsd
  3. Apr 23, 2006 #2

    matt grime

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    No, you can't claim *that* (since it is false; one side is a number, the other is a power series in x), but you can use the series if you do so legitimately.
     
  4. Apr 23, 2006 #3

    HallsofIvy

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    In other words, since 2-n= (2-1)n, yes, if x= 2-1. (Assuming, of course, that the sum converges. Can you show that?)
     
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