# Proof of Scalar Rule for Sequences

$$\def \C {\mathbb{C}}\def \R {\mathbb{R}}\def \N {\mathbb{N}}\def \Z {\mathbb{Z}}\def \Q {\mathbb{Q}}\def\defn#1{{\bf{#1}}}$$
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 $b_n=k$.