Question 75
Let $n$ be a positive integer, $x_1, \dots, x_n$ and $y_1, \dots, y_n$ be positive real numbers satisfying $x_n = n$ and $y_i y_{i+1} \ge 1$ for $1 \le i \lt n$ and $y_n y_1 \ge 1$. Moreover, let $x_0 = 0$.
Determine the minimal possible value of the expression
$$
\sum_{i=1}^{n} \sqrt{(x_i - x_{i-1})^2 + y_i}.
$$
Determine the minimal possible value of the expression
$$
\sum_{i=1}^{n} \sqrt{(x_i - x_{i-1})^2 + y_i}.
$$