(理)已知向量
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,
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(n为正整数),函数
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,设f(x)在(0,+∞)上取最小值时的自变量x取值为a
n.
(1)求数列{a
n}的通项公式;
(2)已知数列{b
n},对任意正整数n,都有b
n•(4a
n2-5)=1成立,设S
n为数列{b
n}的前n项和,求
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;
(3)在点列A
1(1,a
1)、A
2(2,a
2)、A
3(3,a
3)、…、A
n(n,a
n)、…中是否存在两点A
i,A
j(i,j为正整数)使直线A
iA
j的斜率为1?若存在,则求出所有的数对(i,j);若不存在,请你写出理由.
考点分析:
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