Let $\{x_n\}$ be a sequence of real numbers converging to $x$. Show that
$$\lim_{n\to\infty} \frac{1}{n} \sum_{k=1}^n x_k = x .$$
Let $\{x_n\}$ be a sequence of real numbers converging to $x$. Show that
$$\lim_{n\to\infty} \frac{1}{n} \sum_{k=1}^n x_k = x .$$