题目内容
已知数列
的相邻两项
,
是关于
方程
的两根,且
.
(1)求证:数列
是等比数列;
(2)求数列
的前
项和
;
(3)设函数
,若
对任意的
都成立,求实数
的取值范围.
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(1)求证:数列
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(2)求数列
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(3)设函数
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(1)见解析(2)
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试题分析:(1)由一元二次方程根与系数的关系可得数列
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设
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并注意到:
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(2)由(1)的结果得数列
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(3)由韦达定理:
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所以
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试题解析:(1)∵
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∵
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∴
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∴
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且
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(2)由(1)得
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(3)∵
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∴
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∴
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∴当
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∴
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∴当
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∴
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∴
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综上所述,实数
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