(related to Proposition: Product of a Real Number and a Convergent Real Sequence)
The proposition follows immediately from the corresponding proposition for the product of convergent real sequences. \[\lim_{n\rightarrow\infty} (a_n \cdot b_n)=\lim_{n\rightarrow\infty} a_n \cdot \lim_{n\rightarrow\infty} b_n.\]
if we set \(b_n\) to a constant real number \(b_n:=x\) for all \(n\in\mathbb N\).
