Question 2
Let $a_1,a_2,\ldots,a_n$ be positive real numbers, and let $S_k$ be the sum of the products of $a_1,a_2,\ldots,a_n$ taken $k$ at a time. Show that
$$S_kS_{n-k}\ge\binom nk^2a_1a_2\cdots a_n\qquad(k=1,2,\ldots,n-1).$$
$$S_kS_{n-k}\ge\binom nk^2a_1a_2\cdots a_n\qquad(k=1,2,\ldots,n-1).$$