有若干个数,记作a1,a2,a3,······,an.（详见下）有若干个数,记作a1,a2,a3,······,an.规定a2=1/1-a,a3=1/1-a2,······,an=1/1-an-1.若当a1=-½时,试计算a2,a3,a4,a1000和a1001的值.

Question

有若干个数,记作a1,a2,a3,······,an.（详见下）
有若干个数,记作a1,a2,a3,······,an.规定a2=1/1-a,a3=1/1-a2,······,an=1/1-an-1.若当a1=-½时,试计算a2,a3,a4,a1000和a1001的值.

Answer 1

a1=-1/2,a2=1/(1-a1)=1/(1+1/2)=2/3,a3=1/(1-a2)=1/(1-2/3)=3,a4=1/(1-a3)=1/(1-3)=-1/2,……
该数列是以3为周期的数列,则
a2=2/3
a3=3
a4=-1/2
a1000=a997=...=a1=-1/2
a1001=a998=...=a2=2/3
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