What precendece do big $n$-ary operators have in relation to others? Suppose I have: $$\sum_{i=1}^n i^2 + 8$$
I would assume that the $8$ is part of the summables, so we'd get: $$8n + \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6} + 8n$$
So I'd guess the sigma eats everything on the right up to the equals sign? What happens when there's two big sigmas involved? Is:
$$ \sum_{i=1}^n 2i + \sum_{j=1}^n 3j = \left(\sum_{i=1}^n 2i\right) + \left(\sum_{j=1}^n 3j\right) = \frac{5n(n+1)}{2} $$ or $$ \sum_{i=1}^n 2i + \sum_{j=1}^n 3j = \sum_{i=1}^n \left(2i + \sum_{j=1}^n 3j\right) = \frac{n(3n^2+5n+2)}{2} $$
I would assume the first. But assuming notation conventions is not very healthy and as a newcomer to academia I'm having trouble finding anything concrete.
Is there anything set in stone about this? And are there any differences between the precedence of the big sigma and other big operators such as $\prod$, $\bigcup$ and others?