I have lots of doubts (questions) on how to best present my findings.

I'm not sure if most writers use the horizontal $1/(2n)$ to keep the line narrow, or the vertical $\frac{1}{2n}$, which widens the line.

Also, may I use the future tense at will on a math paper (e.g., "we will prove that X, Y, and Z, etc.")? A guy with uwaterloo told me to avoid future tense and passive voice, which doesn't made much sense to me.

I know there isn't an absolute truth to go by, but there must be some standards or best practices?

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    I think egreg would tell you "use $1/(2n)$ only in cooking recipes" :) – CarLaTeX Aug 25 '18 at 7:07
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    Related tex.stackexchange.com/q/135725/35864 – moewe Aug 25 '18 at 7:16
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    @CarLaTeX To the contrary, 1/(2n) is correct. It can also be 1/2n provided it's explained at least once in the paper, in order to clear up possible ambiguities in precedence of operations. – egreg Aug 25 '18 at 9:27
  • @egreg without \frac? – CarLaTeX Aug 25 '18 at 9:42
  • @CarLaTeX Don't confuse algebra with nicefrac. ;-) – egreg Aug 25 '18 at 10:11

Off topic, but in inline text, always use \(...\) instead of $...$. Similarly, use \[...\] and not $$...$$.

To answer your question: I would prefer 1/2n most of the times, as it can usually be understood as meaning 'one divided by 2n', though I understand that it can be frowned upon by some. I think this is not that big of a problem if you make sure that, when you really mean 'half times n', use some other type of notation such as 0.5n or, better, \tfrac{1}{2} n (the \tfrac command is made for exactly this purpose). On the other hand 1/(2n) is really excessive and I would never use it. You can also consider simply \tfrac{1}{2n} but that can make the fraction too small to be readable, but at least it preserves line spacing unlike \frac{1}{2n} (or worse, \dfrac). This has the advantage of never causing confusion.

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    While I agree that \[...\] is preferable to $$...$$ (tex.stackexchange.com/q/503/35864), there are not that many strong reasons to prefer \(...\) over $...$ (see tex.stackexchange.com/q/510/35864). I must say that I find 1/2n for 1/(2n) dangerous and would not recommend it. – moewe Aug 25 '18 at 9:05
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    Isn't \tfrac simply \frac in text mode (similarly \dfrac for display mode)? So using \frac and \tfrac should not make any difference in inline math. – TeXnician Aug 25 '18 at 9:21
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    And btw: The OP did explicitly ask about 1/(2n) and not (1/2)n. – TeXnician Aug 25 '18 at 9:22
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    note that there is a big difference between comparing $/\( and $$/\[ . $$ is not supported latex syntax at all and should not be used, conversely $ is fully supported and equivalent to \( apart from different error behaviour. I think it would be best if you removed the first paragraph. – David Carlisle Aug 25 '18 at 10:57
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    also your comment about \tfrac is wrong. \tfrac and \frac give identical layout in this context. – David Carlisle Aug 25 '18 at 10:58

This is purely my opinion, but I feel that $1/(2n)$ is far more stylistically elegant when used in running text. This is discussed more in the first page or so of Chapter 17 of The TeXBook (you know, the one by Knuth).

  • The problem is that at times you have longer equations that need to go inline and it's impossible to not use an actual formula, so that plain standard is disrupted, and I like to stick to the same standard. – user168592 Aug 25 '18 at 17:38
  • @JRS. I'm afraid I don't understand at all what you're trying to say here. – Derek Aug 25 '18 at 19:47
  • I can't draw, sorry, use your imagination. Then again, it's not important anyway. – user168592 Aug 25 '18 at 19:52

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