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科目:高中数学
来源:不详
题型:解答题
数列
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的各项均为正数,
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为其前
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项和,对于任意
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,总有

成等差数列.
(1)求数列

的通项公式;
(2)若b
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=a
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4

(
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), B
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是数列{b
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}的前

项和, 求证:不等式 B
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≤4B

,对任意

皆成立.
(3)令
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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)
(注意:在试题卷上作答无效)
设函数
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.数列
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满足

,

.
(Ⅰ)证明:函数
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在区间
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是增函数;
(Ⅱ)证明:

;
(Ⅲ)设

,整数
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.证明:
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.
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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)
设数列

的前

项和为

,对任意的正整数

,都有
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成立,记

。
(Ⅰ)求数列

与数列

的通项公式;
(Ⅱ)设数列

的前

项和为

,是否存在正整数

,使得
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成立?若存在,找出一个正整数

;若不存在,请说明理由;
(Ⅲ)记

,设数列

的前

项和为

,求证:对任意正整数

都有

。
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科目:高中数学
来源:不详
题型:解答题
设等差数列{
an}的前
n项和为
Sn,且
Sn=
nan+
an—c(
c是常数,
n∈N
*),
a2=6.
(Ⅰ)求
c的值及{
an}的通项公式;
(Ⅱ)证明:

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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)已知各项均为正数的数列{
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}的前n项和满足
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,且
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(1)求{

}的通项公式;(5分)
(2)设数列{

}满足

,并记

为{
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}的前n项和,
求证:

. (7分)
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科目:高中数学
来源:不详
题型:解答题
设函数

,数列

的通项

满足

.
(1)求数列

的通项公式;(2)判定数列{
a n }的单调性.
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科目:高中数学
来源:不详
题型:单选题
等差数列的前4项依次是
a,
a+1,2
a+3,2
b-3,则
a、
b的值为 ( )
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