在等差数列{
an}中,它的前n项和为S
n,已知
.
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科目:高中数学
来源:不详
题型:解答题
(本小题满分15分)已知
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(Ⅰ)求
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的表达式;
(Ⅱ)定义正数数列
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,证明:数列

是等比数列;
(Ⅲ)令
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成立的最小
n值.命题人:袁卫刚 校对人:沈秋华
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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)已知数列
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是首项为1公差为正的等差数列,数列
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是首项为1的等比数列,设
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,且数列
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的前三项依次为1,4,12,
(1)求数列
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、
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的通项公式;
(2)若等差数列
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的前
n项和为S
n,求数列
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的前
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项的和T
n.
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科目:高中数学
来源:不详
题型:解答题
在数列
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中,
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,且对任意
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.
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,
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,
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成等差数列,其公差为
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。
(Ⅰ)若
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=
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,证明
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,
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,
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成等比数列(
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)
(Ⅱ)若对任意
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,
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,
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,
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成等比数列,其公比为
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。
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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)设
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,方程
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有唯一解,已知
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,且
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(1)求数列
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的通项公式;
(2)若
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,求和
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;
(3)问:是否存在最小整数
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,使得对任意
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,有
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成立,若存在;求出
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的值;若不存在,说明理由。
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科目:高中数学
来源:不详
题型:单选题
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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,则数列
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的通项公式为( )
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科目:高中数学
来源:不详
题型:单选题
若
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是等差数列,满足
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,则有 ( )
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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)
设数列
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中的每一项都不为0。
证明:
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为等差数列的充分必要条件是:对任何
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,都有
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。
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