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y2005=用含x的代数式表

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y2005= 用含x的代数式表

Answer 1

y2=1/[1-x/(x-1)]=1-x
y3=1/[1-(1-x)]=1/x
y4=1/(1-1/x)=x/(x-1)=y1
所以是三个一循环
2005÷3余数是1
所以y2005=y1=x/(x-1)