1 . 在数列
中,
,且对任意的
,
、
、
构成
为公差的等差数列.
(1)求证:
、
、
成等比数列;
(2)求数列
的通项公式;
(3)设
,试问当
时,数列
是否存在极限?若存在,求出其值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c96788577cf6bec6dc77aa39b7e4af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f766fe39702fecd2b6c21855757907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93be7ab21cfc858530a289bf0df381c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c19c544c7df445f84ce7da0a901b00c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0eee3171fa7223e87af0fa95abfd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd5b6b78b5b764e6d0a7db5af0f9fee.png)
您最近一年使用:0次
2 . 设数列
是等差数列,且公差为d,若数列
中任意(不同)两项之和仍是该数列中的一项,则称该数列是“封闭数列”.
(1)若
,求证:该数列是“封闭数列”;
(2)试判断数列
是否是“封闭数列”,为什么?
(3)设
是数列
的前n项和,若公差
,试问:是否存在这样的“封闭数列”,使
;若存在,求
的通项公式,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71661efbd38645dd04a5c93ed6bc32c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f069c238e1d9239fd3913b228965460f.png)
(2)试判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3770337011cf6ee188d3dac48303bed6.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c81d6206a09006901987c51d7532cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54d6777bfac3060e53da2ff964e5b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2019-11-06更新
|
232次组卷
|
2卷引用:上海市晋元高级中学2019-2020年高二上学期9月阶段反馈数学试题
名校
解题方法
3 . 数列
的前
项和为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9aa8c8737223748f099a5c437f3a2cb.png)
(1)写出
的值,并求
的通项公式;
(2)正项等差数列
的前
项和为
,且
,并满足
,成等比数列.
(i)求数列
的通项公式
(ii)设
,试确定
与
的大小关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9aa8c8737223748f099a5c437f3a2cb.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed529240a883f68f0921e818addeb9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)正项等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b6f02731cfe96d404a446d0b8bccc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975a03319e38805eb6e5baa4febe03a4.png)
(i)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf5c50376dddd9144cc896a76b1aab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
您最近一年使用:0次
2020-02-07更新
|
487次组卷
|
2卷引用:上海市晋元高级中学2015-2016学年高二上学期期中数学试题