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I am currently writing a question about an infinite product I got stuck on trying to solve. I realized that I have not actually proven that it converges, something I also do not know how to do.

I see a few ways I could go about this:

  1. I could ask my original problem with the assumption that it converges
  2. I could first ask whether or not it converges in a post and, if it does, write another question asking for help finding what it converges to
  3. I could ask both about whether or not it converges and what it converges to in the same post

I know Stack Exchange wants only one question per post but I feel like the questions are too similar to be split up. What should I do?

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    $\begingroup$ I would ask the first question on its own. The answers you get may include stuff about the convergence, in which case you get both answers for the price of one question. Otherwise ask the second question and link it to the first, explaining that the new one is a continuation of the earlier one. $\endgroup$ Feb 3 at 19:14
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    $\begingroup$ Whatever you do, don't ask about solving an infinite product. One solves an equation, or a problem, but not an infinite product (nor a question). One may evaluate an infinite product, or answer or settle a question about an infinite product, or determine the convergence of an infinite product. $\endgroup$ Feb 3 at 20:35
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    $\begingroup$ While the above is a perfectly correct comment on mathematical linguistics, I don't think "whatever you do, don't ask" is good advice! $\endgroup$
    – N. Virgo
    Feb 14 at 7:34
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    $\begingroup$ Anyway, I think "does this converge and if so what does it evaluate to?" is a single question by any reasonable definition - I wouldn't worry about it. $\endgroup$
    – N. Virgo
    Feb 14 at 7:37
  • $\begingroup$ Is math.stackexchange.com/questions/4856300/… the question in question? $\endgroup$ Feb 17 at 21:28

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I often give the advice on multiple part problem Questions that there needs to be a clear relationship among the parts such that a solution or progress on one will likely benefit a solution on some of the others.

As @N.Virgo remarked, "does this converge and if so what does it evaluate to?", is a reasonable way to frame the Question that spotlights the connection between parts in your example.

Other cases might be better presented with a more detailed discussion. Articulating what connections are known or suspected can provide important context for Readers to respond to.

The splitting of a limit problem into "does the limit exist?" and "if so, what is the limit value?" is an important step and guards against thinking we have evaluated a limit when our deduction is based on assuming a limit exists. See for example this old Question.

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