Real numbers/Convergent sequences/Rules/3/Fact/Proof/Exercise

Let ${\left(x_n\right)}_{n\in \mathbb{N}}$ be a real convergent sequence and $c\in ℝ$. Show that the sequence ${(c\cdot x_n)}_{n\in \mathbb{N}}$ is also convergent and

$\underset{n\to \mathrm{\infty }}{lim}(c\cdot x_n)=c\cdot \left(\underset{n\to \mathrm{\infty }}{lim}{x}_n\right)$

holds.

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