TITLE: Showing a sequence convergence
QUESTION [6 upvotes]: Let $a_1,a_2>0$ and $a_{n+1}=\cfrac{2}{a_{n-1}+a_{n}}(n\ge2)$,
How to prove $a_n$ is convergent?

REPLY [9 votes]: This is AMM(problem, E3388), maybe have other methods.