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For the ratio test: If all a(n) are positive then why absolute value is needed within the lim? That is, we should omit the positive condition, and let the test extend to the alternating series, such as a(n+1) = -a(n)/2.

How about the alternating series test? Fishie2610 (talk) 00:05, 12 June 2009 (UTC)[reply]

If i'm not mistaken Leibniz also have an important test regarding convergence which says that if An->0 and An>An+1 then the sum of An*(-1^n) should converge. —Preceding unsigned comment added by 84.229.138.185 (talk) 15:38, 29 July 2010 (UTC)[reply]

limit of the summand

the article says if the limit of the summand is zero the sequence of partial sums if cauchy. I'm not sure of this, but AFAIK if a sequence is cauchy in the reals it converges, but that doesnt happen to the harmonic series, even if it's summand tends to zero. — Preceding unsigned comment added by 186.18.76.220 (talk) 22:58, 15 November 2011 (UTC)[reply]

It says so here http://en.wikipedia.org/wiki/Convergent_series#Cauchy_convergence_criterion — Preceding unsigned comment added by 186.18.76.220 (talk) 23:01, 15 November 2011 (UTC)[reply]

I can't resolve this, but it ought to be resolved. Both of the above comments seem to be correct. In addition, is it reallyl true that if the limit is undefined then the sum diverges? No source is given. --editeur24 (talk) 05:05, 18 December 2020 (UTC)[reply]

terms must be positive or not

this is a huge discrepancy between this page and the test descriptions on the convergent series page. Someone please fix / clarify. — Preceding unsigned comment added by 75.186.86.53 (talk) 11:32, 18 March 2016 (UTC)[reply]

The polishing of the statement of the Leibniz criterion

The language used to state the criterion is rather verbose. I suggest that we apply the bullet point style for the statement, like the other criteria on the page. 13:27, 4 January 2017 (UTC)~ Appleuseryu (talk) 13:27, 4 January 2017 (UTC)[reply]

Should the Absolute convergence be called a test and have its own section?

Absolute convergence test

Every absolutely convergent series converges.

Should this be its own section, as it is presently, and is it really a "test"? It is a useful remark-- should it be put elsewhere?

--editeur24 (talk) 05:10, 18 December 2020 (UTC)[reply]

@@ Line 31: / Line 31: @@
 The language used to state the criterion is rather verbose. I suggest that we apply the bullet point style for the statement, like the other criteria on the page.
 :27, 4 January 2017 (UTC)~ [[User:Appleuseryu|Appleuseryu]] ([[User talk:Appleuseryu|talk]]) 13:27, 4 January 2017 (UTC)
+== Should the Absolute convergence be called a test and have its own section?  ==
+===[[Absolute convergence|Absolute convergence test]]===
+Every [[absolutely convergent]] series converges.
+-----------------------------------------------------------
+:Should this be its own section, as it is presently, and is it really a "test"? It is a useful remark-- should it be put elsewhere?
+:--[[User:Editeur24|editeur24]] ([[User talk:Editeur24|talk]]) 05:10, 18 December 2020 (UTC)