Hi I dont think this is a particularly high quality question: How to expand $\frac{x^n-1}{x-1}$? but the asker very clearly had trouble with how to perform a computation/carry out an algorithm/know what algorithm to even use.

At least 2 of the comments here missed the point of the question entirely and were focused on proving the identity works as opposed to showing how to carry out the division (which is what the OP was requesting).

Unfortunately the question is now closed but was this considered a valid closure? It feels very premature for me and moreover I am concerned that a lot of the downvotes and close votes also were users who missed the point of the question. The linked answer also misses the point of the question as it merely proves the identity but doesn't show how to carry out the expansion.

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    $\begingroup$ The OP had provided almost no context and did not (yet) reply to any comments, I cannot tell what kinds of algorithm/technique do they have in mind? The post is now closed as a duplicate which solve their literal question. If they are not satisfied with the duplicate (I don't know, say they don't like induction), they could update their post, indicating which methods they want to use and what difficlties do they encounter. From there others might consider reopening the post. $\endgroup$ Aug 29, 2022 at 17:51
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    $\begingroup$ Update: the OP just replied in the post that they are satisfied with the method (long division) suggested by one of the user. $\endgroup$ Aug 29, 2022 at 17:53
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    $\begingroup$ So we know for fact at this point that the close as duplicate was invalid and that linked answer is not helpful. Moreover we know for fact that at least half the commenters were off and that would suggest that many of the close voters were also off. I think this is a failure of the closing system. I agree the question isn't great but the way the community acted here is wrong. $\endgroup$ Aug 29, 2022 at 18:19
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    $\begingroup$ @SidharthGhoshal I am confused. I don't see anything in the comments which indicates that the asker is dissatisfied with the linked duplicate. All I see is that they are happy with the answer which was provided in the comments. $\endgroup$
    – Xander Henderson Mod
    Aug 29, 2022 at 18:41
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    $\begingroup$ Also, the question is a FAQ. In five minutes of searching, I found three more closely related questions (including one which it seems I answered). I am not sure that I see the value in keeping around yet another copy of that question. $\endgroup$
    – Xander Henderson Mod
    Aug 29, 2022 at 18:48

1 Answer 1


That Question is now deleted. It was a very terse post about "expanding" the quotient into a geometric series:

$$ \frac{x^n - 1}{x-1} = x^{n-1} + x^{n-2} + \ldots + x + 1 $$

Their two-line post mentions something about expanding using the binomial theorem, and the first Comment actually presents three ways to think about the identity. That is the one the OP wound up thanking, so perhaps you are reading too much into your interpretation (you also left a Comment) about "how to perform a computation" vs. "how to prove".

So you are right, it is not "a particularly high quality question". And the asker seems to have gotten unstuck with the help of comments on it. I think we should feel that Math.SE was successful in aim of helping students of mathematics at all levels here. Retaining the Question would not further our goal of becoming a repository of all mathematical knowledge (in my opinion), not merely because of its duplicative nature, but because the point of the problem was not clear to most of its Readers (by your judgement).

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    $\begingroup$ i think there is a high probability another student might look up "how to expand (x^n -1)/(x-1)" and not find the question, and if we retained the question there would have been at least one post which doesn't merely prove the result is valid but show how it is valid by carrying out long division in a step by step process. At least that was my reason for feeling this question should stay but be cleaned up $\endgroup$ Aug 29, 2022 at 21:06
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    $\begingroup$ This might involve more subtlety about the English language than most users here care about, but when I read the question I was totally unsure about what they meant by "expand", and although they seemed to be satisfied with the "do long division" answer, I still don't see how that relates to "expanding". $\endgroup$
    – JonathanZ
    Aug 30, 2022 at 1:23

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