已知數(shù)列

中,

,前

項的和為

,對任意的

,

,

,

總成等差數(shù)列.
(1)求

的值并猜想數(shù)列

的通項公式

(2)證明:

.
試題分析:(1)

,

,

總成等差數(shù)列,所以有

,令

,令

,令

4分
由已知可得

(

)
所以

(

) ,從第二項開始構(gòu)成等比數(shù)列,公比為

,



8分
(2)

12分
點評:本題已知條件主要是關(guān)于

的關(guān)系式,由此求通項時借助于

此外第二小題還可借助于第一問的結(jié)論,結(jié)合數(shù)學(xué)歸納法猜想并證明
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:單選題
如果

為各項都大于零的等差數(shù)列,公差

,則
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知數(shù)列{ a
n }滿足a
1=

,且對任意的正整數(shù)m,n,都有a
m+n= a
m + a
n,則

等于( )
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

是等差數(shù)列,且滿足:

,

;數(shù)列

滿足

.
(1)求

和

;
(2)記數(shù)列

,若

的前

項和為

,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
已知數(shù)列

是等差數(shù)列,其中

,

。
(1)求數(shù)列

的通項公式;
(2)求

…

的值。
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

是一個等差數(shù)列,

是其前

項和,且

,

.
(1)求

的通項

;
(2)求數(shù)列

的前10項的和

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

的前

項和

,數(shù)列

滿足

(1)求數(shù)列

的通項公式

;(2)求數(shù)列

的前

項和

;
(3)求證:不論

取何正整數(shù),不等式

恒成立
查看答案和解析>>