(15分)数列{a
n},a
1=1,
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(1)求a
2,a
3的值;
(2)是否存在常数
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,使得数列
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是等比数列,若存在,求出
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的值;若不存在,说明理由;
(3)设
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,
解:(1)
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(2)设
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,
即
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故
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∴
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又
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使得数列
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是等比数列
(3)证明:由(1)得
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∴
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,故
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∵
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∴
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
,现证
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当n=2时,
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,
故n=2时不等式成立,当
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得
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∵
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