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Counterintuitive Convergent Series

  1. Nov 12, 2007 #1
    [SOLVED] Counterintuitive Convergent Series

    1. The problem statement, all variables and given/known data

    One of my new textbooks in mathematical analysis makes a very strange claim (not sure if it was a true claim or some random historical anecdote) for a convergent series in one of its short sections on the history of mathematics, which I am baffled about.

    2. Relevant equations

    [tex]1 + q + q^2 + q^3 + ... = \frac{1}{1-q}[/tex]

    [tex]q = 2 \rightarrow [/tex]

    [tex]1 + 2 + 4 + 8 +.... = -1[/tex]


    3. The attempt at a solution

    It can either be one of two explanations in my mind; it is either completely false in some way (undefined or misapplication of a theorem or wrong approach) or only applies in the realm of mathematics and you do not get -1 apples if you keep adding them together.

    Thank you for your time.
    Last edited: Nov 12, 2007
  2. jcsd
  3. Nov 12, 2007 #2


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    I do hope the textbook mentions that not all values of q are permitted for that expression.
    The left side converges only when |q|<1.
  4. Nov 12, 2007 #3
    Indeed, I finally managed to find the passage it was referring to. Thanks for your help.
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