Question 137
Suppose that the real numbers $a_1, a_2, \dots, a_n$ satisfy $a_1 + a_2 + \dots + a_n = 0$. Prove
$$
\max_{1 \le i \le n} a_i^2 \le \frac{n}{3} \sum_{i=1}^{n-1} (a_i - a_{i+1})^2.
$$
(pose by Zhu Huawei)
$$
\max_{1 \le i \le n} a_i^2 \le \frac{n}{3} \sum_{i=1}^{n-1} (a_i - a_{i+1})^2.
$$
(pose by Zhu Huawei)