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Suppose that $\{ x_n \}_{ n = 1 }^\infty$ is a converging sequence of real numbers with $\lim_{ n \to \infty } x_n = x$. Define $$ y_n = \frac{ x_1 + \cdots + x_n }{ n } $$ Show that $\lim_{ n \to \infty } y_n = x$.

I'm not really sure where to start.

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