Question 190
Let $n \geqslant 2$ be an integer and let $x_{1}, \ldots, x_{n}$ be positive real numbers such that $x_{1} x_{2} \cdots x_{n}=1$. Show that
$$
\frac{1}{n-1+x_{1}}+\frac{1}{n-1+x_{2}}+\cdots+\frac{1}{n-1+x_{n}} \leqslant 1
$$
$$
\frac{1}{n-1+x_{1}}+\frac{1}{n-1+x_{2}}+\cdots+\frac{1}{n-1+x_{n}} \leqslant 1
$$