\sum_{m \leq i < n}
then all the text can stay the same. This would be much clearer for people like me who want to understand SymPy, while still being clear for people who understand Karr's summation convention.
Text before the 5th example can then be simplified:
"Note that Karr defines all sums with the upper limit being exclusive, but this does not affect the summation convention. Indeed we have:"
Similar improvements for sympy.concrete.products.Product.
Martin