数列题~已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...求证:数列{1/(an-1)}为等差数列

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数列题~已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...求证:数列{1/(an-1)}为等差数列
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数列题~已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...求证:数列{1/(an-1)}为等差数列
数列题~已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...
已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...
求证:数列{1/(an-1)}为等差数列

数列题~已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...已知数列{an}满足:a1=2,an+1=2-1/an,n=1,2,3,4...求证:数列{1/(an-1)}为等差数列
代入递推式a=2-1/a
1/(a-1)=1/(2-1/a-1)=a/(a-1)
=(a-1+1>)/(a-1)
=1/(a-1)+1
所以{1/(an-1)}为等差数列
如果你不熟悉,就换元b=1/(a-1)
b=1/(a-1)
把a用b表示,a用b表示就行了