So i was googling about the formal definition of summation and couldn't find anything, except for the wikipedia (formal, i suppose) definition:
Summation may be defined recursively as follows: $$ \begin{align} \sum_{i=a}^b g(i) &= 0, \text{for } b<a \\ \sum_{i=a}^b g(i) &= g(b) + \sum_{i=a}^{b-1} g(i), \;\text{for } b \geq a \end{align} $$
My problem is: this is valid for all $a$, $b$, $i$, and $g(i)$ or there is some condition behind it that I didn't see?