(本小題滿分12分)
正項數(shù)列

的首項為

,

時,

,數(shù)列

對任意

均有

(1)若

,求證:數(shù)列

是等差數(shù)列;
(2)已知

,數(shù)列

滿足

,記數(shù)列

的前

項和為

,求證

.
(1)利用定義法來證明即可。
(2)根據(jù)錯位相減法來求和并比較大小。
練習冊系列答案
相關(guān)習題
科目:高中數(shù)學
來源:不詳
題型:填空題
觀察下表:
1
2 3 4
3 4 5 6 7
4 5 6 7 8 9 10
…………
則第__________行的各數(shù)之和等于

查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:單選題
等差數(shù)列{a
n}中,a
1,a
2,a
3分別是下表第一、二、三行中的某一個數(shù),且a
1,a
2,a
3中的任何兩個數(shù)不在下表的同一列。
| 第一列
| 第二列
| 第三列
|
第一行
| 2
| 3
| 5
|
第二行
| 8
| 6
| 14
|
第三行
| 11
| 9
| 13
|
則a
4的值為
A.18 B.15 C.12 D.20
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:單選題
等差數(shù)列{a
n}的通項公式為a
n=2n+1,其前n項和為S
n,則{

}前10項和為
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:解答題
等差數(shù)列

的首項

,前n項和

,當

時,

。問n為何值時

最大?
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:解答題
(本小題滿分12分)a
2,a
5是方程x
2-12x+27=0的兩根,數(shù)列{

}是公差為正數(shù)的等差數(shù)列,數(shù)列{

}的前n項和為

,且

=1-

(1)求數(shù)列{

},{

}的通項公式;
(2)記

=


,求數(shù)列{

}的前n項和Sn.
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:填空題
已知4個命題:
①若等差數(shù)列

的前n項和為

則三點

共線;
②命題:“

”的否定是“

”;
③若函數(shù)

在(0,1)沒有零點,則k的取值范圍是

④

是定義在R上的奇函數(shù),

的解集為(

2,2)
其中正確的是
。
查看答案和解析>>