(本題滿分12分)
已知數(shù)列

滿足

,

,(

,

).
(1)求證:數(shù)列

是等差數(shù)列;
(2)若數(shù)列

的前

項和為

,且

恒成立,求

的最小值.


是以

為首項,

為公差的等差數(shù)列。 (4分)
(2)由(1):


(6分)

①
則

②
①—②,得


(9分)
由

恒成立。
得

恒成立,

是單增數(shù)列,
且


(12分)
練習(xí)冊系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本題滿分12分)
直線

過點P

(

斜率為

,與直線

:

交于點A,與

軸交于點B,點A,B的橫坐標(biāo)分別為

,記

.
(Ⅰ)求

的解析式;
(Ⅱ)設(shè)數(shù)列

滿足

,求數(shù)列

的通項公式;
(Ⅲ)在(Ⅱ)的條件下,當(dāng)

時,證明不等式

.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知數(shù)列

中,


,對于函數(shù)

有

(1)證明數(shù)列

為等比數(shù)列,并求

的通項公式
(2)若

,求和

查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題共14分)
數(shù)列

的前n項和為

,點

在直線

上.
(I)求證:數(shù)列

是等差數(shù)列;
(II)若數(shù)列

滿足

,求數(shù)列

的前
n項和

(III)設(shè)

,求證:

查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分13分)
已知函數(shù)

(I)求函數(shù)

的通項公式;
(Ⅱ)設(shè)

的前n項和S
n。
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
等差數(shù)列

的各項均為正數(shù),

,前

項和為

,

為等比數(shù)列,

,且


.
(1)求

與

;(2)求和:

.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
等差數(shù)列

中,第2、3、7項成等比數(shù)列,求公比q.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分14分)
已知數(shù)列

(1)試求
a的取值范圍,使得

恒成立;
(2)若

;
(3)若

,求證:

查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
用

三個字母組成一個長度為


個字母的字符串,要求由

開始,相鄰兩個字母不同. 例如

時,排出的字符串可能是

或

;

時排出的字符串可能是


(如圖).若記長度為

個字母的字符串中,以字母

結(jié)尾的所有字符串的種數(shù)為

,
如:

則數(shù)列

的前

項之和為
.

查看答案和解析>>