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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

,数列

满足:
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,
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,
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.
(Ⅰ) 求证:数列

是等差数列;数列

是等比数列;(其中
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;
(Ⅱ) 记

,对任意的正整数

,不等式

恒成立,求

的取值范围.
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科目:高中数学
来源:不详
题型:解答题
(本小题满分8分)
已知

是一个公差大于0的等差数列,且满足

.
(Ⅰ)求数列

的通项公式:
(Ⅱ)等比数列

满足:

,若数列

,求数列

的前n项和
.
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科目:高中数学
来源:不详
题型:解答题
已知数列

的前
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项和为
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,点
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均在函数

的图象上
(1)求数列

的通项公式
(2)若数列

的首项是1,公比为

的等比数列,求数列

的前

项和

.
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科目:高中数学
来源:不详
题型:解答题
(本小题16分)如图所示,数列

的前
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项的和
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,

为数列

的前

项的和,且

.

(1)求数列

、

的通项公式;
(2)找出所有满足:
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的自然数

的值(不必证明);
(3)若不等式

对于任意的
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,

恒成立,求实数

的最小值,并求出此时相应的

的值.
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科目:高中数学
来源:不详
题型:解答题
(本小题满分14分)
已知数列

为等差数列,且

,

.
(1) 求数列

的通项公式;
(2) 令

,求证:数列

是等比数列;
(3)令

,求数列

的前

项和

.
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