$\lim x_n = a \in \mathbb{R}$, $\lim y_n = b \in \mathbb{R}$. Prove that $\lim \frac{x_1y_n + x_2y_{n-1} + \cdots + x_ny_1}{n} = ab$
Find the limit $\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}$