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.
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?