Question 9
(MON) Let $a_1,a_2,\ldots,a_n$ be positive real numbers such that $a_1+a_2+\cdots+a_n\lt 1$. Prove that
$$\frac{a_1a_2\cdots a_n[1-(a_1+a_2+\cdots+a_n)]}{(a_1+a_2+\cdots+a_n)(1-a_1)(1-a_2)\cdots(1-a_n)}\le\frac1{n^{n+1}}.$$
$$\frac{a_1a_2\cdots a_n[1-(a_1+a_2+\cdots+a_n)]}{(a_1+a_2+\cdots+a_n)(1-a_1)(1-a_2)\cdots(1-a_n)}\le\frac1{n^{n+1}}.$$