TITLE: Should I include obvious steps in mathematical paper?
QUESTION [8 upvotes]: I am writing a formal school paper (by formal I mean, with an abstract, a bibliography and $20$ pages in length) on mathematics (it is called "Extended Essay", for those having knowledge of the International Baccalaureate) and I was wondering whether I should include algebra steps as in $$\frac{(2k+1)^{-2}}{1-(2k+1)^{-2}} = \frac {1}{4k(k+1)}.$$ In fact I can do this in my head and I am sure that the external examiner will not have the slightest problem understanding steps. However, I only fear that when you don't show any steps it is as if you copied it from a book or so, which is not case.
In general for academic papers (like important undergraduate mathematical projects), should I include such steps or other non-algebraic steps that are sort of obvious and that the reader can pretty much understand even by grabbing pen and paper in the worst case?
Thanks in advance.

REPLY [7 votes]: I am not a mathematician, but I teach engineering and computer science, and I've read quite a number of papers and reports from students. I don't know if this is just me being particularly lazy, but I'd rather avoid having to decode things that are only "sort of" obvious, or that I need pen and paper to get through.
When a student has worked with a project, maybe for months, many things seem obvious to that student, so they omit them from the report or paper. Perhaps they even feel ashamed to put such very simple things in their text. But the things that are obvious to someone who has just spent weeks or months on them, sometimes are much less obvious to another reader.