对于数列

,定义

为数列

的一阶差分数列,其中

;对

,定义

为

的

阶差分数列,其中

.
(1)若数列

的通项公式为

,分别求出其一阶差分数列

、二阶差分数列

的通项公式;
(2)若数列

首项

,且满足

,求出数列

的通项公式

及前

项和

.
(1)


=

。

。
(2)由

与

得

,所以

所以

,则

是等差数列。
所以

,所以

。
所以

①
则

②
由①-②得


所以

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
设数列

的首项

,


⑴求

的通项公式(

已知)
⑵设

,证明:


。
查看答案和解析>>
科目:高中数学
来源:不详
题型:单选题
直线

与直线

关于点

对称,则

的等比中项为 ( )
A.-2 | B.2 | C. | D. |
查看答案和解析>>
科目:高中数学
来源:不详
题型:解答题
设

是等差数列,

是各项都为正数的等比数列,且

,

,

(Ⅰ)求

,

的通项公式;
查看答案和解析>>
科目:高中数学
来源:不详
题型:解答题
已知数列

中,

,点

在直线

上,其中

…。
(1)令

,证明数列

是等比数列;
(2)设

分别为数列

、

的前

项和,证明数列

是等差数列。
查看答案和解析>>
科目:高中数学
来源:不详
题型:解答题
数列

中,

,

,

.
(Ⅰ)证明:数列

是等比数列,并求

;
(Ⅱ)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)已知数列

满足

,

,

.
(1)求证:

是等比数列;
(2)求证:设

,且

对于

恒成立,
求

的取值范围.
查看答案和解析>>