已知函数f(x)=4x-2/x+1(x≠1,x∈R) 数列{an}满足a1=a(a≠-1,a∈R),a (n+1)=f(an)(n∈N*)当a1=4时,记bn=an-2/an-1(n∈N*),证明数列{bn}是等比数列,并求出通项公式an

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已知函数f(x)=4x-2/x+1(x≠1,x∈R) 数列{an}满足a1=a(a≠-1,a∈R),a (n+1)=f(an)(n∈N*)当a1=4时,记bn=an-2/an-1(n∈N*),证明数列{bn}是等比数列,并求出通项公式an
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已知函数f(x)=4x-2/x+1(x≠1,x∈R) 数列{an}满足a1=a(a≠-1,a∈R),a (n+1)=f(an)(n∈N*)当a1=4时,记bn=an-2/an-1(n∈N*),证明数列{bn}是等比数列,并求出通项公式an
已知函数f(x)=4x-2/x+1(x≠1,x∈R) 数列{an}满足a1=a(a≠-1,a∈R),a (n+1)=f(an)(n∈N*)
当a1=4时,记bn=an-2/an-1(n∈N*),证明数列{bn}是等比数列,并求出通项公式an

已知函数f(x)=4x-2/x+1(x≠1,x∈R) 数列{an}满足a1=a(a≠-1,a∈R),a (n+1)=f(an)(n∈N*)当a1=4时,记bn=an-2/an-1(n∈N*),证明数列{bn}是等比数列,并求出通项公式an
f(x)=(4x-2)/(x+1),a (n+1)=f(an)(n∈N*)
所以a(n+1)= (4an-2)/(an+1),
b(n+1)= (a(n+1)-2)/(a(n+1)-1)
=[(4an-2)/(an+1)-2]/[ (4an-2)/(an+1)-1]
=[(4an-2) -2(an+1)]/[ (4an-2) -(an+1)]
=2(an-2)/[3 (an-1)]
=2/3*bn,
数列{bn}是等比数列,公比是2/3,首项b1=(a1-2)/(a1-1)=2/3.
∴bn=(2/3)^n.
即(an-2)/(an-1) =(2/3)^n.
即得an=(2^n-2*3^n)/(2^n-3^n).

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