已知y1=x/x-1（x不等于0)且y2=1/1-y1,y3=1/1-y2,y4=1/1-y3``````yn=1/1-yn-1,则y2012=用含x的代数表示

Question

已知y1=x/x-1（x不等于0)且y2=1/1-y1,y3=1/1-y2,y4=1/1-y3``````yn=1/1-yn-1,则y2012= 用含x的代数表示

Answer 1

数学之美团为你解答
y₁ = x/(x-1)
y₂ = 1/(1 - y₁) = 1/[1 - x/(x-1)] = 1 - x
y₃ = 1/(1-y₂) = 1/x
y₄ = 1/(1-y₃) = x/(x-1) = y₁
由上可知,y的表达式是循环出现的
每过3个重复一次
2012÷3 余 2
所以 y₂₀₁₂ = y₂ = 1 - x