Convergence/Divergence and Reordering of an Alternating Series

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Main Question or Discussion Point

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?
 
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Answers and Replies

  • #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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