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a recursive sequence concerning Fibonacci

Source: China second round 2006 p2

March 10, 2012
algebra unsolvedalgebra

Problem Statement

Let x,yx,y be real numbers. Define a sequence {an}\{a_n \} through the recursive formula a0=x,a1=y,an+1=anan−1+1an+an−1, a_0=x,a_1=y,a_{n+1}=\frac{a_na_{n-1}+1}{a_n+a_{n-1}}, Find ana_n.
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