已知数列{An}满足:A1=3 ,An+1=(3An-2)/An,n属于N*.1)证明:数列{(An--1)/(An--2)}为等比数列,并求数列{An}的通项公式;2)设Bn=(1/(An--2))-n,求数列{Bn}的前n项和
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![已知数列{An}满足:A1=3 ,An+1=(3An-2)/An,n属于N*.1)证明:数列{(An--1)/(An--2)}为等比数列,并求数列{An}的通项公式;2)设Bn=(1/(An--2))-n,求数列{Bn}的前n项和](/uploads/image/z/729972-36-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3%3AA1%3D3+%2CAn%2B1%3D%283An-2%29%2FAn%2Cn%E5%B1%9E%E4%BA%8EN%2A.1%EF%BC%89%E8%AF%81%E6%98%8E%EF%BC%9A%E6%95%B0%E5%88%97%7B%EF%BC%88An--1%EF%BC%89%2F%EF%BC%88An--2%EF%BC%89%7D%E4%B8%BA%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%B9%B6%E6%B1%82%E6%95%B0%E5%88%97%7BAn%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%9B2%EF%BC%89%E8%AE%BEBn%3D%281%2F%EF%BC%88An--2%EF%BC%89%29-n%2C%E6%B1%82%E6%95%B0%E5%88%97%7BBn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C)
已知数列{An}满足:A1=3 ,An+1=(3An-2)/An,n属于N*.1)证明:数列{(An--1)/(An--2)}为等比数列,并求数列{An}的通项公式;2)设Bn=(1/(An--2))-n,求数列{Bn}的前n项和
已知数列{An}满足:A1=3 ,An+1=(3An-2)/An,n属于N*.1)证明:数列{(An--1)/(An--2)}为等比数列,并求
数列{An}的通项公式;
2)设Bn=(1/(An--2))-n,求数列{Bn}的前n项和
已知数列{An}满足:A1=3 ,An+1=(3An-2)/An,n属于N*.1)证明:数列{(An--1)/(An--2)}为等比数列,并求数列{An}的通项公式;2)设Bn=(1/(An--2))-n,求数列{Bn}的前n项和
(1)设f(x)=(3x-2)/x,方程f(x)=x有1,2俩个根
A(n+1)-1=(3An-2)/An-1=2(An-1)/An
(A(n+1)-1) / (A(n+1)-2)=2(An-1)/(An *( A(n+1)-2)
=2(An-1)/(An-2)
叠乘法
(A(n+1)-1) / (A(n+1)-2)=2^n *(a1-1)/(a1-2)
=2^(n+1)
An=(2^(n+1)-1)/(2^n-1)
(2)Bn=2^n-1-n
分开求2^n +(-1-n)
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