Combination Theorem for Sequences/Multiple Rule

Real Sequences
Let $\sequence {x_n}$ be a sequences in $\R$.

Let $\sequence {x_n}$ be convergent to the following limit:


 * $\ds \lim_{n \mathop \to \infty} x_n = l$

Let $\lambda \in \R$.

Then:

Complex Sequences
Let $\sequence {z_n}$ be a sequence in $\C$.

Let $\sequence {z_n}$ be convergent to the following limit:


 * $\ds \lim_{n \mathop \to \infty} z_n = c$

Let $\lambda \in \C$.

Then: