Question 24
Determine the smallest real number $a$ satisfying
$$
a \ge \sum_{k=1}^{n} a_k \cos(a_1 + \dots + a_k),
$$
for all positive integers $n$ and all positive real numbers $a_1, \dots, a_n$ that add up to at most $\pi$.
$$
a \ge \sum_{k=1}^{n} a_k \cos(a_1 + \dots + a_k),
$$
for all positive integers $n$ and all positive real numbers $a_1, \dots, a_n$ that add up to at most $\pi$.