Question 68
Let $(a_n)_{n \ge 1}$ be an increasing bounded sequence of real numbers. Evaluate
$$
\lim_{n \to \infty} (2a_n - a_1 - a_2)(2a_n - a_2 - a_3) \cdots (2a_n - a_{n-2} - a_{n-1})(2a_n - a_{n-1} - a_1).
$$
$$
\lim_{n \to \infty} (2a_n - a_1 - a_2)(2a_n - a_2 - a_3) \cdots (2a_n - a_{n-2} - a_{n-1})(2a_n - a_{n-1} - a_1).
$$