Question 122
Suppose that $x_{1}, x_{2}, x_{3}, \ldots, x_{n}$ are real numbers between $0$ and $1$ with sum $s$. Prove that
$$
\sum_{i = 1}^{n} \frac{x_{i}}{s + 1 - x_{i}} + \prod_{i = 1}^{n}(1 - x_{i}) \leq 1.
$$
$$
\sum_{i = 1}^{n} \frac{x_{i}}{s + 1 - x_{i}} + \prod_{i = 1}^{n}(1 - x_{i}) \leq 1.
$$