Simpson’s rule is given (in my textbook) as such:
It becomes difficult to express this in a way that a computer algebra system can assist you when the definition is given in this format. By re-expressing the definition with two summations, however, this becomes much easier to gain computational assistance.
Why my textbook doesn’t see fit to explain this is quite beyond my understanding. It illustrates a clever use of summations and expressions in subscripts to achieve “all the odd elements” and “all the even elements,” which is a fundamental tool that will enhance a student’s abilities in the future.