Cesaro Means of a Convergent Real Sequence Converge to Its Limit

In the setting of The Real Numbers: Standing Notation and Background, let $(a_{k})_{k\in\mathbb{N}}$ be a sequence of real numbers that converges to $a\in\mathbb{R}$.

(Cesaro means)¶ The sequence of averages $\bigl(\tfrac{1}{n}\sum_{k=1}^{n}a_{k}\bigr)_{n\in\mathbb{N}}$ converges to $a$.