Question 72
Let $x_1, x_2, \dots, x_n$ ($n \ge 2$) be real numbers greater than $1$. Suppose that $|x_i - x_{i+1}| \lt 1$ for $i = 1, 2, \dots, n-1$. Prove that
$$
\frac{x_1}{x_2} + \frac{x_2}{x_3} + \dots + \frac{x_{n-1}}{x_n} + \frac{x_n}{x_1} \lt 2n - 1
$$
$$
\frac{x_1}{x_2} + \frac{x_2}{x_3} + \dots + \frac{x_{n-1}}{x_n} + \frac{x_n}{x_1} \lt 2n - 1
$$