Luc, I guess I have been stated the three of constraints in my question is not clear. ( easily cause misunderstanding, especially the First constraint ) :
From your last post I think you are looking for continued fraction. Both Mathcad 15 and Prime a function to easily calculate continued fractions.
confrac will give a list of each of numbers in a continued fraction
confrac,faction will show the continued fraction
Thanks for your time, Tietjee. But I don't know how to create a continued fraction with alternate sign, so I have to create by hand as the following :