已知,数列
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是公比为
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的等比数列,
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.
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(1)求数列
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的通项公式;
(2)令
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,若数列
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的前
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项和
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,求证:
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(1)
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, ………………1分
又数列
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的等比数列。
从而
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………………6分
(2)由
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,
两式相减得:
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,
所以
所以:
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科目:高中数学
来源:不详
题型:解答题
(本小题满分12分)已知等差数列
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中,公差
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,其前
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项和为
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,且满足
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,
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.
(1)求数列
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的通项公式;
(2)设
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(
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),数列
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的前
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项和为
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,求证:
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;
(3)是否存在常数
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(
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),
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使得数列
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为等差数列?若存在,试求出
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;若不存在,说明理由.
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科目:高中数学
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已知集合
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.
(1)是否存在实数
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,使得集合
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中所有整数
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的元素和为28?若存在,求出符合条件的
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,若不存在,请说明理由。
(2)若以
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为首项,
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为公比的等比数列前
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项和记为
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,对于任意的
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,均有
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,求
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的取值范围。
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(理)设数列
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满足
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,且对任意的
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,点
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都有
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,则
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的前
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项和
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为( )
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科目:高中数学
来源:不详
题型:解答题
(本题满分14分)
已知
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是递增数列,其前
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项和为
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,
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,
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且
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,
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.
(Ⅰ)求数列
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的通项
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;
(Ⅱ)是否存在
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,使得
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成立?若存在,写出一组符合条件的
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的值;若不存在,请说明理由;
(Ⅲ)设
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,若对于任意的
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,不等式
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恒成立,求正整数
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的最大值.
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科目:高中数学
来源:不详
题型:解答题
(本小题满分12分)
设各项为正的数列
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的前
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项和为


且满足:
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(Ⅰ)求
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(Ⅱ)求
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(Ⅲ)设
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且
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求证:
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科目:高中数学
来源:不详
题型:填空题
数列
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和
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的公共项由小到大排列成数列
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,则
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的通项公式
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=____________前n项和
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=_______________。
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