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A(n+1)-An=根号下(2/3(An+An+1))
左右平方后化简得
3(An+1)^2+3An^2-6AnAn+1=2(An+An+1) ---- (1)
当n≥2时
3(An)^2+3An-1^2-6AnAn-1=2(An+An-1) ---- (2)
(1)-(2)得
3(An+1^2-An-1^2)-6An(An+1-An-1)=2(An+1-An-1) --- (3)
因为An+1-An>0 所以 An+1≠An-1
(3)式左右约去An+1-An-1后得
3(An+1+An-1)-6An=2
(An+1-An)-(An-An-1)=2/3
所以{An+1-An}成等差数列
1年前
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