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科目:高中数学
来源:不详
题型:解答题
已知数列

的相邻两项

是关于

的方程

的两根,且

(1)求证:数列

是等比数列;
(2)求数列

的前

项和

;
(3)若

对任意的

都成立,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
(本题满分16分)定义
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,

,…,

的“倒平均数”为

(

).已知数列

前

项的“倒平均数”为

,记

(

).
(1)比较

与

的大小;
(2)设函数

,对(1)中的数列

,是否存在实数

,使得当

时,

对任意

恒成立?若存在,求出最大的实数

;若不存在,说明理由.
(3)设数列

满足

,

(

且

),

(

且

),且

是周期为

的周期数列,设

为

前

项的“倒平

均数”,求

.
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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

的前

项和为

,且

是

与2的等差中项,数列

中,

,点

在直线

上.
⑴求

和

的值;
⑵求数列

的通项

和

;
⑶ 设

,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
已知点

(

)满足

,

,且点

的坐标为

.
(Ⅰ)求经过点

,

的直线

的方程;
(Ⅱ)已知点

(

)在

,

两点确定的直线

上,求数列

通项公式.
(Ⅲ)在(Ⅱ)的条件下,求对于所有

,能使不等式


成立的最大实数

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)已知函数

(

是自然对数的底数)

(1)求

的最小值;
(2)不等式

的解集为P, 若
求实数

的取值范围;
(3)已知

,是否存在等差数列

和首项为

公比大于0的等比数列

,使数列

的前n项和等于

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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{
an}中,
a1 =1,前
n项和为S
n,且点(
an,
an+1)在直线
x-
y+1=0上.
计算

+

+

+…

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科目:高中数学
来源:不详
题型:单选题
已知数列

的前

项和

,对于任意的

,都满足

,
且

,则

等于( )
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