We often have questions of related to various convergence tests for infinite series, such as:

  • Does the following series converge or diverge?
  • What is an example showing that this convergence test is stronger than the other one?
  • Is it true that this condition is sufficient for the series to be convergent?

Such questions certainly belong into tag. However, I thought whether a separate tag for this type of questions would be useful.

But before suggesting a new tag, I looked into tag-excerpts and tag-wikis of some already existing tags, since - at least to my understanding - they describe the intended usage of the specific tags. I found several tags, which might be used for the type of questions I described above. I will quote from the tag-infos, emphasis is mine.

The tag-excerpt for divergent-series says:

Questions on whether certain series diverge, and how to deal with divergent series using summation methods such as Ramanujan summation and others.

(Perhaps it is worth mentioning that a separate tag exists. There are is also . And the tag is sometimes used for questions on summability methods.)

The tag-wiki for convergence says:

This tag is for questions about Convergent Sequences and Series and their existence.

(There is certainly a space for improvement in this tag-info, too.)

Based on tag-infos it seems that both these tags could be suitable for questions I described. And they are indeed used in this way: see https://math.stackexchange.com/search?q=[convergence]+series or https://math.stackexchange.com/search?q=[divergent-series]+test.

This situation is certainly not optimal. We have two different tags which seem suitable for the questions about testing convergence of a series. Typically when such question is asked, the OP does not know in advance whether the series is convergent or divergent, so it would be difficult to choose a tag based on this.

What is, in your opinion, a good solution to this. Should we create a new tag? Should we use some of already existing tags? Or is the tag sufficient and we do not need to differentiate this particular type of questions? How would you tag question asking whether some given series converges or not?


1 Answer 1


Regular calculus problems of this kind should be tagged as and (and maybe if that is the topic). No need to add or split between convergent and divergent series.

The tag is useless. It contains everything from numeric series to numeric sequences to improper integrals to sequences in metric/topological spaces to limit theorems in probability to convergence in $L^p$ sense to abstract normed and topological vector spaces. This tag is a lost cause.

(As an aside, and are in better shape thanks to more specific names.)

Using the tag makes sense if it's specific to summation methods. This should be made clear in the tag wiki by deleting the part "questions on whether certain series diverge". Indeed, asking whether some series diverges is no different from asking whether that series converges.

  • $\begingroup$ I certainly agree with "No need to split between convergent and divergent series there." (What I wrote in my question is basically describing how the situation looks like.) If I understand your post correctly, you are also saying that there is no need to have a specific (convergence-tests) tag for questions of this type.. $\endgroup$ Jul 7, 2015 at 22:26
  • $\begingroup$ The original intent of the tag (divergent-series) might have been summability methods. On the other hand, if this is a primary use of this tag, then we should probably be able to choose a better name for it. $\endgroup$ Jul 7, 2015 at 22:28
  • $\begingroup$ I clarified that I don't see any need for convergence-test tag. I think the name divergent-series is not that bad; most of the questions in there actually deal with divergent series. Hardy's book "Divergent series" comes to mind; I think the title describes the topic. $\endgroup$
    – user147263
    Jul 7, 2015 at 22:38
  • $\begingroup$ You are right, that is a classical reference for summability methods. BTW MO also has divergent-series tag. And there are a few questions on this site which use (regularization) for this topic. $\endgroup$ Jul 7, 2015 at 22:44

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