Question 27
Let $x_1, x_2, \dots, x_n$ be positive real numbers and $n \ge 3$. Prove the inequality
$$
\frac{x_1 x_3}{x_1 x_3 + x_2 x_4} + \frac{x_2 x_4}{x_2 x_4 + x_3 x_5} + \dots + \frac{x_{n-1} x_1}{x_{n-1} x_1 + x_n x_2} + \frac{x_n x_2}{x_n x_2 + x_1 x_3} \le n-1
$$
$$
\frac{x_1 x_3}{x_1 x_3 + x_2 x_4} + \frac{x_2 x_4}{x_2 x_4 + x_3 x_5} + \dots + \frac{x_{n-1} x_1}{x_{n-1} x_1 + x_n x_2} + \frac{x_n x_2}{x_n x_2 + x_1 x_3} \le n-1
$$