Quoting from this answer on the main meta site (with a tip of the hat to Martin Sleziak):
We had discussed this before, but deferred until there was a problem - it seems we now have a problem :)
The new rules (also apply to undelete votes):
- 10k rep users get 5 deletion votes per day on questions they don't own, increasing by 1 vote per extra 1,000 reputation up to 30 votes per day - deletion rules on questions one does own are still in effect.
- Popular questions require more deletion votes to be deleted, at a ratio of 20:1 - a question's popularity is defined as: question score + top-scored answer score. For example, a question with (question score 15 + top answer score 5 = 20) will require 4 deletion votes (3 base votes + 1 popularity vote).
- The maximum number of delete votes needed will not exceed 10.
Note that the above rules apply only to questions; answers take 3 votes, regardless of score.
At the time that this question was deleted, it had a net score of $0$, and the top answer (which was written by J. Heller) had a net score of $+6$. This gives that question a "popularity" of $6$, which is well shy of the threshold required for an additional delete vote. Therefore, from a purely mechanical point of view, the answer to the question "How could this question be deleted?" is that
- five users felt that the question failed to meet the quality standards of the site and voted to close it, and
- the question was insufficiently popular to require more than three delete votes, and three users voted to delete it.
However, I believe that the asker of this meta question is also interested in the following:
While the asker of this meta question does not explicitly ask why the question was deleted, it seems implicit form the phrasing of the question that this is also of concern. The question was closed for lacking context. The canned close reason reads
Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.
Thus those who voted to close the question (including myself) felt that it did not meet the consensus standards for quality. The asker of this meta question asserts that "The question is short, but it is something that many people have probably asked themselves when studying Riemann integrals." I do not disagree with that statement, but I see nothing in the meta-thread on asking a question which indicates that a question being common, on its own, is sufficient to justify retaining that question on this website.
While one can read the close reason and the "how to ask a good question" thread, it might be helpful to elucidate specific concerns about the question being discussed here.
Strike one against the question is that the actual question is in the title only, and not contained anywhere in the body of the question. This makes the question less accessible to mobile readers. However, this is not a big deal, and can be easily fixed.
More importantly, the question lacks much in the way of context. In this case, the asker has two bits of notation,
$$
\lim_{n\to\infty} \left( \sum_{i=1}^{n} x_i \right)
\qquad\text{and}\qquad
\sum_{i=1}^{\infty} x_i,
$$
and wants to know how they differ. However, the asker doesn't actually explain what either piece of notation means. The first is, arguably, clear. However, the second really does require some explanation. In most elementary texts with which I am familiar, the definition is something like
Definition: Let $(x_i)_{i=1}^{\infty}$ be a sequence, and suppose that the sequence $(S_n)$ converges to $S$, where $S_n$ is defined to be
$$ S_n = \sum_{i=1}^{n} x_i. $$
Then define
$$ \sum_{i=1}^{\infty} x_i = S. $$
From such a definition, the distinction between the two notations is immediately clear (i.e. the infinite series is only defined if the limit of the partial sums exists). Of course, other texts may have slightly different definitions, so it is incumbent upon the asker to explain what the notation is meant to mean. Something like this was communicated to the asker by this comment, which was posted several days before the question was closed (hence the asker had time to add context to their question).
Finally, I think that the question is unclear. Specifically, I find the reference to Riemann integration a little confusing in this context. Ideally, the asker would provide some context for that comment by giving an example. More generally, if one encounters notation which is confusing, then one should give one (or more!) example(s) of the notation being used. If they are confused about the notation being used in the context of a Riemann sum or integral, then they should specifically spell out an example in which this confusion is made manifest.
Moreover, as has been pointed out in the comments below, the question has five answers, three of which ([1],[2],[3]) seem to have a common interpretation of the question, and the other two of which seem to have distinct interpretations ([4],[5]). The fact that the answerers cannot agree on the correct interpretation of the question is, to me, evidence that the question is unclear.
Other close-voters may have additional reasons for believing that the question fails to meet the quality standards of the site. In any event, the question was closed, and the close reason is, essentially, that the question is of low quality.
Once a question has been closed, it is eligible for deletion. I would argue that if question is closed then, after a certain amount of time, the question ought to be deleted unless there is a compelling reason to keep it on the cite. Compelling reasons might include the following:
The asker (or someone else) improves the question so that it meets the site's guidelines, in which case the question should be reopened.
The question is closed as a duplicate, but is otherwise of high quality (such questions can serve as roadsigns for future askers).
The question has historic or cultural significance for this site (my go-to example of such a question is the Batman question, which is hardly even a question; the question and its answers, however, received thousands of upvotes and hundreds of thousands of pageviews, so there may be some reason to keep it around).
The question has attracted a truly stellar answer. In general, I feel that questions should be judged in isolation. However, sometimes a very poor question attracts a phenomenally good answer. In such cases, it may be worth keeping the question around in order to preserve the answer. I would argue that such cases are quite rare, and that a better solution is to ask a new version of the question, then ask the moderators to merge the old question with the new, improved question.
This list is likely not exhaustive, but it should give a sense of when not to delete a question. In the current situation, the question was closed for lacking context (i.e. it was closed because it was considered to be of low-quality), and was not subsequently improved. As the question is not of historical significance to the site, nor are any of the answers particularly exceptional, the question was deleted.
