Talk:Convergent series

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[edit] Mistake?

The statement of the Cauchy criterion for convergence is incorrect, but I am not sure how it should be changed. David Radcliffe 19:35, 30 November 2005 (UTC)

I think it is correct just fine. :) It says that the sequence of partial sums is a Cauchy sequence, which is equivalent to the sequence being convergent. Oleg Alexandrov (talk) 00:20, 1 December 2005 (UTC)

I'm sorry, but it does not currently state that the partial sums form a Cauchy sequence. I will post a correction. David Radcliffe 02:50, 1 December 2005 (UTC)

You are right, it was close to Cauchy sequences, but not quite. The harmonic series would have satisfied that criterion which was wrong. I also posted a formulation after you fixed that part. Oleg Alexandrov (talk) 03:10, 1 December 2005 (UTC)

Thanks. I like your formulation using double limits. David Radcliffe 03:39, 1 December 2005 (UTC)

[edit] More convergence tests

Unde the convergence tests section, the article could also mention the n-th term test, the p-series, the geometric series, and most importantly, the power series. If anyone willing to add these tests, please do so. Otherwise I'll add them in later on.--Rejnal 04:33, 15 March 2006 (UTC)

Yes, please add them. If you feel you have a lot of detail to put in, you could also create new articles about those topics. Cheers, Oleg Alexandrov (talk) 04:37, 15 March 2006 (UTC)

Can't the limit comparison test also establish divergence iff b sub n diverges. The test is inconclusive if the limit does not exist. I think it should be mentioned. Good luck! Cronholm144 23:35, 6 May 2007 (UTC)