Question 47
Let $x_1, x_2, \dots, x_{2020}$ be non-negative real numbers such that
$$
x_i + x_{i+1} + x_{i+2} \le 2 \quad \text{for } i = 1, 2, \dots, 2018.
$$
Show that
$$
\sum_{i=1}^{2018} x_i x_{i+2} \le 1009.
$$
$$
x_i + x_{i+1} + x_{i+2} \le 2 \quad \text{for } i = 1, 2, \dots, 2018.
$$
Show that
$$
\sum_{i=1}^{2018} x_i x_{i+2} \le 1009.
$$