Finite sum (${\sum }_{i=1}^n{a}_i$)

A finite sum adds finitely many terms, for example ${\sum }_{i=1}^n{a}_i=a_1+\cdots +a_n$ for a positive integer $n$. The empty sum is the additive identity. In an abelian group, the associative property and commutativity of the abelian group make the result independent of grouping and order.