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Using a notebook as a notebook.

Apart from having made a reasonably thorough study of the Mathematica core language and notebook interface I am new to Mathematica and remain at somewhat of a loss as to how to go about using it as a substitute for a pen and paper notebook. This would encompass the following use-cases: (1) rote transcription from a textbook at the advanced undergraduate to graduate level in addition to my own "between the lines" embellishments (i.e. filling in of "gaps"); (2) a complete rewrite of a proof from a text book; (3) original material; (4) possibly some integration with Mathematica's symbol manipulation, theorem proving/verification capabilities. 

Perhaps a concrete example would help clarify my goals. The case I have in mind involves a summation over a subset of a sequence satisfying some condition, but I cannot find a way to represent this in Mathematica, which seems to in every case require a numerical index of summation, with the index to at the bottom right of the sigma instead of directly under it, which latter would be the natural location for the desired set-theoretical specification of the summands.

Another, more general, issue I am having is whether to enter a given piece of exposition as a text cell or as a math cell, and whether certain palettes have a text vs. a math "bias." Unfortunately, I lack the patience for instructional videos and cannot seem to find any conventional, text (i.e., html or notebook) based documentation of the palettes. I contacted support regarding this and they are currently taking their time responding.

I welcome your advice.

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