Sum of Even Integers is Even/Proof 2

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

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

where:
 * $\forall k \in \closedint 1 n: r_k = 2 s_k$

Then:

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