irregular summations in Home/CAS

[Albert Chan]

(10-26-2024 05:59 AM)Wes Loewer Wrote:  Starting with
0. Σ(..., a, b) + Σ(..., b+1, c) = Σ(..., a, c)
...

FYI, there is an implicit increment parameter (= 1).
Above is true only if LHS terms have non-negative elements.

We are ignoring that fact for the 'proof' to continue.
(it is not really a proof, only to make result consistent)

n = b - a + 1
-n = a - b - 1 = (a-1) - (b+1) + 1

n + (-n) = 0      ; elements count
Σ(..., a, b) + Σ(..., b+1, a-1) = 0

Again, above is a sum definition with negative elements count, not a prove.