Question 30
Let $n\ge2$ be an integer, and let positive real numbers $a_0,a_1,\ldots,a_n$ satisfy
$$(a_{k-1}+a_k)(a_k+a_{k+1})=a_{k-1}-a_{k+1}\quad(k=1,\ldots,n-1).$$
Prove that $a_n\lt 1/(n-1)$.
$$(a_{k-1}+a_k)(a_k+a_{k+1})=a_{k-1}-a_{k+1}\quad(k=1,\ldots,n-1).$$
Prove that $a_n\lt 1/(n-1)$.