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--
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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
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)
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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