User:Keith.U/Sandbox/Proof 2

Theorem
Let $r$, $s \in \C$ be complex numbers.

Let $\left\langle{ a_n }\right\rangle$ and $\left\langle{ b_n }\right\rangle$ be two complex sequences.

Let $\displaystyle \sum_{n \mathop = 1}^{\infty} a_n$ and $\displaystyle \sum_{n \mathop = 1}^{\infty} n_n$    convergent with sums $a$ and $b$, respectively.

Then $\displaystyle \sum_{n \mathop = 1}^{\infty} \left({ r a_n + s b_n }\right) = ra + sb$.