Question 85
The sequence $(a_n)_{n\ge1}$ is increasing and bounded. Calculate
$$\begin{aligned}\lim_{n\to\infty}\big[&(2a_n-a_1-a_2)(2a_n-a_2-a_3)\cdots\\&\cdot(2a_n-a_{n-2}-a_{n-1})(2a_n-a_{n-1}-a_1)\big].\end{aligned}$$
$$\begin{aligned}\lim_{n\to\infty}\big[&(2a_n-a_1-a_2)(2a_n-a_2-a_3)\cdots\\&\cdot(2a_n-a_{n-2}-a_{n-1})(2a_n-a_{n-1}-a_1)\big].\end{aligned}$$