Question 143
Given an integer $n \ge 2$, determine the maximum value the sum
$$
a_1/a_2 + a_2/a_3 + \dots + a_{n-1}/a_n
$$
may achieve, and the points at which the maximum is achieved, as $a_1, \dots, a_n$ run over all of positive real numbers subject to
$$
a_k \ge a_1 + \dots + a_{k-1}, \quad k = 2, \dots, n.
$$
$$
a_1/a_2 + a_2/a_3 + \dots + a_{n-1}/a_n
$$
may achieve, and the points at which the maximum is achieved, as $a_1, \dots, a_n$ run over all of positive real numbers subject to
$$
a_k \ge a_1 + \dots + a_{k-1}, \quad k = 2, \dots, n.
$$