How should questions about deciding convergence/divergence of a series be tagged?

Question

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 sequences-and-series 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 ramanujan-summation exists. There are is also summation-method. And the tag regularization 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 sequences-and-series 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?

Answer 1

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

The tag convergence 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, weak-convergence and uniform-convergence are in better shape thanks to more specific names.)

Using the tag divergent-series 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.