Question 49
Let $n$ be an integer, $n \ge 2$, and $x_1, x_2, \dots, x_n \in [0, 1]$. Prove that
$$
\sum_{1 \le k \lt l \le n} kx_k x_l \le \frac{n-1}{3} \sum_{k=1}^{n} kx_k.
$$
$$
\sum_{1 \le k \lt l \le n} kx_k x_l \le \frac{n-1}{3} \sum_{k=1}^{n} kx_k.
$$