设

是定义在

上恒不为零的函数,对任意的实数

,都有

,若

,

,(

),则数列

的前

项和

的最小值是( )

由已知,令

,则

,即

,所以

,所以数列

是以

为首项,

为公比的等比数列,则数列

的前

项和

的最小值为

,即

练习册系列答案
相关习题
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

,

,数列

满足

,

.
(1)求证:数列

为等比数列.
(2)令

,求证:

;
(3)求证:

查看答案和解析>>
科目:高中数学
来源:不详
题型:解答题
设数列

的各项均为正数,若对任意的正整数

,都有

成等差数列,且

成等比数列.
(Ⅰ)求证数列

是等差数列;
(Ⅱ)如果

,求数列

的前

项和。
查看答案和解析>>
科目:高中数学
来源:不详
题型:解答题
(本小题满分12分)
在数列

中,

.
(1)求

的值;
(2)求数列

的通项公式;
(3)求

的最大值.
查看答案和解析>>
科目:高中数学
来源:不详
题型:单选题
若数列

满足

,

,则此数列是
A.等差数列 | B.等比数列 |
C.既是等差数列又是等比数列 | D.既非等差数列又非等比数列 |
查看答案和解析>>
科目:高中数学
来源:不详
题型:解答题
(1)设函数

,且数列

满足

= 1,

(
n∈N,

);求数列

的通项公式.
(2)设等差数列

、

的前
n项和分别为

和

,且

,

,

;求常数
A的值及

的通项公式.
(3)若

,其中

、

即为(1)、(2)中的数列

、

的第

项,试求

查看答案和解析>>
科目:高中数学
来源:不详
题型:解答题
已知函数

时,

的值域为

,当

时,

的值域为

,依次类推,一般地,当

时,

的值域为

,其中k、m为常数,且

(1)若k=1,求数列

的通项公式;
(2)项m=2,问是否存在常数

,使得数列

满足

若存在,求k的值;若不存在,请说明理由;
(3)若

,设数列

的前n项和分别为S
n,T
n,求

。
查看答案和解析>>