$$\def \C {\mathbb{C}}\def \R {\mathbb{R}}\def \N {\mathbb{N}}\def \Z {\mathbb{Z}}\def \Q {\mathbb{Q}}\def\defn#1{{\bf{#1}}}$$

**Sum Rule**

Suppose that $(a_n)$ is a convergent sequences with $a_n\to a$. Then

$ka_n\to ka$ for all $k\in \R$.

**Proof**

This will follow from the Product Rule if we take $b_n=k$.

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