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数列an满足2an+an-1-1=0a1=1则a100=

题目详情
数列an满足2an+an-1-1=0 a1=1 则a100=
▼优质解答
答案和解析
令 2An+2t+A(n-1)+t=0
所以 t=-1/3
所以 2An-(2/3) +A(n-1) -(1/3)=0
2*(An- 1/3)=-[A(n-1) -(1/3)]
(An- 1/3)/[A(n-1) -(1/3)]= -1/2
所以 {An -1/3}是公比为 -1/2 的等比数列,首项为2/3
A100 -1/3 =(2/3)*(-1/2)^99
A100=(2/3)*(-1/2)^99 +1/3