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# Alternating series watch

1. Hi, if a series goes to a certain value but keeps alternating signs, can we still say it converges or is it called something else? Thanks.
2. As far as I know, it still 'converges'.
The only thing different is the value it is converging around.

Something may go from 2 to 4 to 2.5 to 3.5 to 2.7 to 3.2 to... converging on 3
but it may also go from 1 to -1 to 0.5 to -.05 to 0.3 to -0.3 to ... converging on 0
3. (Original post by AnonyMatt)
As far as I know, it still 'converges'.
The only thing different is the value it is converging around.

Something may go from 2 to 4 to 2.5 to 3.5 to 2.7 to 3.2 to... converging on 3
but it may also go from 1 to -1 to 0.5 to -.05 to 0.3 to -0.3 to ... converging on 0
Thanks for the reply, I actually meant sequence but you know what i mean . How about if the sequence goes from 0 to +-0.5 like 0, -0.1, 0.15, -0.2.....0.4987, -0.49980, 0.499997675 etc... is that also converging? It probably wouldn't be as random as that but I couldn't actually think of a sequence .
4. (Original post by JBKProductions)
Thanks for the reply, I actually meant sequence but you know what i mean . How about if the sequence goes from 0 to +-0.5 like 0, -0.1, 0.15, -0.2.....0.4987, -0.49980, 0.499997675 etc... is that also converging? It probably wouldn't be as random as that but I couldn't actually think of a sequence .
Umm... I'm not sure. It looks like it was diverging at the start...

But no, if it is alternating towards +-5, then it is not converging, but I'm afraid I don't know what you would call it!

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Updated: March 20, 2011
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