Question 2
Let $a_1,\ldots,a_n$ be positive real numbers, where $n>2$ and $a_1\ne a_n$, forming a nondecreasing sequence ($a_k\le a_{k+1}$ for $1\le k\lt n$) or a nonincreasing sequence ($a_k\ge a_{k+1}$ for $1\le k\lt n$). Let $x,y$ be positive real numbers such that $$\frac xy\ge\frac{a_1-a_2}{a_1-a_n}.$$ Prove that, using cyclic indices $a_{n+1}=a_1$, $a_{n+2}=a_2$, $$\sum_{k=1}^n\frac{a_k}{a_{k+1}x+a_{k+2}y}\ge\frac n{x+y}.$$