Let $\lim_{n\to\infty}a_n$ = a, $\lim_{n\to\infty}b_n$ = b. We need to find $\lim_{n\to\infty}\frac{a_nb_1+a_{n-1}b_2+...+a_1b_1}{n}$.
Find the limit $\lim_{n\to\infty} \frac{x_1 y_n + x_2 y_{n-1} + \cdots + x_n y_1}{n}$