What does it mean to say that a sequence of real numbers $\left(x_{n}\right)$ converges to $x$ ? Suppose that $\left(x_{n}\right)$ converges to $x$. Show that the sequence $\left(y_{n}\right)$ given by

$$y_{n}=\frac{1}{n} \sum_{i=1}^{n} x_{i}$$

also converges to $x$.