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Convergence/Divergence and Reordering of an Alternating Series

  1. Oct 24, 2011 #1
    I was just thinking about the following series:

    1-2+3-4+5...

    I'm not familiar with any other series like this one(other than the alternating harmonic), and I was curious as to whether or not it would be convergent, and if reordering it to

    -1+2-3+4-5....

    would change its convergence.

    If its divergent, which it seems it would be, is it divergent to negative or positive infinity?

    This is probably a basic question, but I'm unable to figure it out right now. Any takers?
     
    Last edited: Oct 24, 2011
  2. jcsd
  3. Oct 24, 2011 #2

    mathman

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    It is divergent to no particular value. It can be made to approach anything by suitable rearrangement. Examples:
    -1+2 = 1, -3+4=1, etc. -> +∞.
    0-1=-1, 2-3=-1, 4-5=-1, etc. -> -∞.
     
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