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](/uploads/image/z/1773284-68-4.jpg?t=%E6%95%B0%E5%88%97%E9%A2%98%7E%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3%EF%BC%9Aa1%3D2%2Can%2B1%3D2-1%2Fan%2Cn%3D1%2C2%2C3%2C4...%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3%EF%BC%9Aa1%3D2%2Can%2B1%3D2-1%2Fan%2Cn%3D1%2C2%2C3%2C4...%E6%B1%82%E8%AF%81%3A%E6%95%B0%E5%88%97%7B1%2F%28an-1%29%7D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97)
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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
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