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2

Part of 2006 China Second Round Olympiad

Problems(2)

a recursive sequence concerning Fibonacci

Source: China second round 2006 p2

3/10/2012
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.
algebra unsolvedalgebra
2006 China Second Round Olympiad Test 1 #2

Source:

9/28/2014
Suppose logx(2x2+x−1)>logx2−1log_x (2x^2+x-1)>log_x 2-1. Then the range of xx is <spanclass=′latex−bold′>(A)</span> 12<x<1<spanclass=′latex−bold′>(B)</span> x>12andx≠1<spanclass=′latex−bold′>(C)</span> x>1<spanclass=′latex−bold′>(D)</span> 0<x<1{ <span class='latex-bold'>(A)</span>\ \frac{1}{2}<x<1\qquad<span class='latex-bold'>(B)</span>\ x>\frac{1}{2} \text{and} x \not= 1\qquad<span class='latex-bold'>(C)</span>\ x>1\qquad<span class='latex-bold'>(D)</span>}\ 0<x<1\qquad
logarithms