解题方法
1 . 已知数列
满足:
, .请从①
;②
中选出一个条件,补充到上面的横线上,并解答下面的问题:
(1)求数列
的通项公式;
(2)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1d454ca32c5e179412a30f75d72a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0a0da8453da51b1f9a00985490b9c8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa9ea4e9d50fc5cd747a119be8fc471c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448a657084816b158e2002b29ac42af9.png)
您最近一年使用:0次
2 . 设数列
满足:
,
,且对任意的
,都有
.
(1)从下面两个结论中选择一个进行证明.
①数列
是等差数列;
②数列
是等比数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082ecba4ca64c4e683f484eb1c98a1a4.png)
(1)从下面两个结论中选择一个进行证明.
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eceeb945e82d73d017fb40a2bd3525e.png)
(2)求数列
![](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)
您最近一年使用:0次
2023-12-08更新
|
506次组卷
|
2卷引用:江苏省泰州市泰兴中学2023-2024学年高二上学期阶段测试(三)数学试题
名校
解题方法
3 . 已知数列
的前
项和为
,
,
.
(1)求
的通项公式;
(2)设
,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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3dbfcbd58f87a4fbbadd3021dda8ba1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea451369913dd8fd4945fe54ba1d2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f931530588b8bc46bb89c73f93f12cb.png)
您最近一年使用:0次
2023-11-14更新
|
1002次组卷
|
2卷引用:江苏省泰州市姜堰中学2023-2024学年高三上学期期中数学试题
名校
解题方法
4 . 已知数列
满足
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
(1)求证:数列
是等差数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b71f853a5f52f0c085431c60a4d4af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91dcf5da1c722a8a328ea8d0d789238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7706e0dba93c9f25c28bc8b01de44b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-01-14更新
|
989次组卷
|
3卷引用:江苏省泰州市2022-2023学年高三上学期期末数学试题
名校
解题方法
5 . 记
为正项数列
的前n项和,且
.
(1)求
的通项公式;
(2)记数列
的前n项积为
,证明:数列
是递增数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584293c94385d782623501c23fa5c4a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9690bede7f74b60556ac410e29828d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
您最近一年使用:0次
2022-10-05更新
|
1394次组卷
|
2卷引用:江苏省泰州市泰兴中学2022-2023学年高三上学期第一次调研考试数学试题
6 . 已知数列
满足
,
,
.
(1)设
,
,求证:数列
为等差数列;
(2)求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb65a03cbd622222d928f911f9ac3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb882a35c06bed888729cd3b0cf0bad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f5a133982e755a5cd52ef21bf95d251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460051e994f6e23bd5810a40f7bd21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
您最近一年使用:0次
2022-04-19更新
|
1027次组卷
|
4卷引用:江苏省泰州市兴化市2022届高三下学期4月模拟考试数学试题
江苏省泰州市兴化市2022届高三下学期4月模拟考试数学试题湖北省天门中学2022届高三下学期适应性考试(二)数学试题(已下线)2022年高考考前20天终极冲刺攻略(三)【数学】(新高考地区专用)(5月31日)广东省清远市华侨中学2023届高三上学期10月月考数学试题
7 . 数列
的各项均为正数,
,当
时,
.
(1)证明:
是等差数列,并求数列
的通项公式;
(2)设
,数列
前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171c857f8174ff2cabf361a86dd59d23.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79084ddfb3a4934513e6916b8af3721c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51a52131e33641767a7a65ebb67b8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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/fc1f5d407c0e99344ed5f0f5926c5d22.png)
您最近一年使用:0次
2022-11-10更新
|
1225次组卷
|
7卷引用:江苏省泰兴中学、南菁高级中学、常州市第一中学三校2022-2023学年高三上学期第二次联考数学试题
8 . 记数列
的前
项和为
,
,
,
.
(1)证明数列
为等差数列,并求通项公式
;
(2)记
,求
.
![](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/738dc67ac3b150252a964d1ffe3dfa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9bd0eb8aeaf86ee27f809b60699c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c10862c194e56f9f93d7a3295ed0f7.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b46156f515c26c96997054b141ed35b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f710b0e6ccca316852bf3a94f68135.png)
您最近一年使用:0次
2022-03-21更新
|
3035次组卷
|
12卷引用:江苏省泰州市姜堰中学2021-2022学年高二上学期期中数学试题
江苏省泰州市姜堰中学2021-2022学年高二上学期期中数学试题山西省太原市太原师范学院附属中学、师苑中学2021-2022学年高二上学期12月月考数学试题江苏省南京市中华中学2021-2022学年高三上学期12月月考数学试题(已下线)专题4.6 分组求和法求和-2021-2022学年高二数学特色专题卷(人教A版2019选择性必修第二册)(已下线)专题4.7 数列(基础巩固卷)-2021-2022学年高二数学特色专题卷(人教A版2019选择性必修第二册)江苏省南京市中华中学2021-2022学年高二上学期12月月考数学试题(已下线)第19节 数列求和(已下线)专题24 等差数列及其前n项和-3河北省邢台市第一中学2022-2023学年高二上学期第三次月考数学试题(已下线)4.2.3 等差数列的前n项和-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)吉林省洮南市第一中学2022-2023学年高二下学期阶段性考试数学试题(已下线)专题03 等差数列(二十三大题型+过关检测专训)(4)
9-10高三·上海·阶段练习
9 . 已知数列
中,
且点
在直线
上.
(1)求数列
的通项公式;
(2)若函数
,求函数
的最小值;
(3)设
表示数列
的前
项和.试问:是否存在关于
的整式
,使得
对于一切不小于
的自然数
恒成立? 若存在,写出
的解析式,并加以证明;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b47ecee651ae4b4ecf7a8a0bffd2535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e7d8fb05d18b61b51e70ff1abed7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26251f92a46b07a3bfe81394b6e502d6.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2851cb9ffb602b4cec7ccd01e35dd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c1a72253f12e053bb095752c0355cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2851cb9ffb602b4cec7ccd01e35dd95.png)
您最近一年使用:0次