已知F1(x)=2/(1+x),定义Fn+1(x)=F1[Fn(x)],an=[Fn(0)-1]/[Fn(0)+2],则数列an的通项公式是

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已知F1(x)=2/(1+x),定义Fn+1(x)=F1[Fn(x)],an=[Fn(0)-1]/[Fn(0)+2],则数列an的通项公式是已知F1(x)=2/(1+x),定义Fn+1(x)=F1[F

已知F1(x)=2/(1+x),定义Fn+1(x)=F1[Fn(x)],an=[Fn(0)-1]/[Fn(0)+2],则数列an的通项公式是
已知F1(x)=2/(1+x),定义Fn+1(x)=F1[Fn(x)],an=[Fn(0)-1]/[Fn(0)+2],则数列an的通项公式是

已知F1(x)=2/(1+x),定义Fn+1(x)=F1[Fn(x)],an=[Fn(0)-1]/[Fn(0)+2],则数列an的通项公式是

F1(0)=2/(1+0)=2
则a1=[2-1]/[2+2]=1/4
Fn(0)=F1[Fn-1(0)]=2/[1+Fn-1(0)]
则:an
=[Fn(0)-1]/[Fn(0)+2]
=[2/(1+Fn-1(0)) -1]/[2/(1+Fn-1(0)) +2]
=[2-(1+Fn-1(0))]/[2+2(1+Fn-1(0))]
=[1-F...

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F1(0)=2/(1+0)=2
则a1=[2-1]/[2+2]=1/4
Fn(0)=F1[Fn-1(0)]=2/[1+Fn-1(0)]
则:an
=[Fn(0)-1]/[Fn(0)+2]
=[2/(1+Fn-1(0)) -1]/[2/(1+Fn-1(0)) +2]
=[2-(1+Fn-1(0))]/[2+2(1+Fn-1(0))]
=[1-Fn-1(0)]/[4+2Fn-1(0)]
=(-1/2) [Fn-1(0)-1]/[Fn-1(0)+2]
=(-1/2) a(n-1)
故{an}公比是(-1/2)的等比数列
则:an
=a1(-1/2)^(n-1)
=(1/4)*(-1/2)^(n)/[-1/2]
=(-1/2)*(-1/2)^n
=(-1/2)^(n+1)

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