microsoft_office_word wrote: Given a sequence of positive real numbers such that $a_{n+2}=\frac{2}{a_{n+1}+a_{n}}$.Prove that there are two positive real numbers $s,t$ such that $s \le a_n \le t$ for all $n$ positive integers Let $u>\max(a_1,a_2,\frac 1{a_1},\frac 1{a_2})$ so that : $\frac 1u<a_1<u$ and $\frac 1u<a_2<u$ Immediate induction implies $\frac 1u<a_n<u$ $\forall n\in\mathbb N$ Q.E.D.