a1=1/2,3(1+an+1)/1-an=2(1+an)/1-an+1,anan+1=0,bn=an+12-an2,求1)an,bn通项,2)证明bn中任意三项

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a1=1/2,3(1+an+1)/1-an=2(1+an)/1-an+1,anan+1=0,bn=an+1*2-an*2,求1)an,bn通项,2)证明bn中任意三项
a1=1/2,3(1+an+1)/1-an=2(1+an)/1-an+1,anan+1=0,bn=an+1*2-an*2,求1)an,bn通项,2)证明bn中任意三项

a1=1/2,3(1+an+1)/1-an=2(1+an)/1-an+1,anan+1=0,bn=an+1*2-an*2,求1)an,bn通项,2)证明bn中任意三项
1.
3(1-a²(n+1))=2(1-a²n)
(1-a²(n+1))/(1-a²n)=2/3
令tn=(1-a²n)
则tn为等比数列,首项,t1=3/4,公比为2/3
tn=3/4*(2/3)^(n-1)
(1-a²n)=3/4*(2/3)^(n-1)
a²n=1-3/4*(2/3)^(n-1)
an=+,-√[1-3/4*(2/3)^(n-1)]
an•（an+1）0
所以n为奇时,an>0,an=√[1-3/4*(2/3)^(n-1)]
n为偶时,an

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