Sum of Even Integers is Even/Proof 2

Proof
Let $S = \left\{{r_1, r_2, \ldots, r_n}\right\}$ be a set of $n$ even numbers.

By definition of even number, this can be expressed as:
 * $S = \left\{{2 s_1, 2 s_2, \ldots, 2 s_n}\right\}$

where:
 * $\forall k \in \left[{1 \,.\,.\, n}\right]: r_k = 2 s_k$

Then:

Thus, by definition, $\displaystyle \sum_{k \mathop = 1}^n r_k$ is even.