## Algebra 2 (1st Edition)

$\displaystyle \sum_{i=1}^{n}(a_{i}+b_{i})=$ $=(a_{1}+b_{1})+(a_{2}+b_{2})+......+(a_{n}+b_{n})$ ... addition is associative and commutative ... (we can remove the parentheses and group terms in any order) $=(a_{1}+a_{2}+...+a_{n})+(b_{1}+b_{2}+...+b_{n})$ ... both parentheses can be written in summation notation $=(\displaystyle \sum_{i=1}^{n}a_{i})+(\sum_{i=1}^{n}b_{i})$