1 . 已知正项数列
中,
,且
.
(1)求数列
的通项公式;
(2)
,证明,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed0367987c04be8561bcecd097dd981.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64550bd5d557facd691696e60b27510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79ee9bb88c0d1b069a7924162a84ab8.png)
您最近一年使用:0次
2 . 在数列
和
中,
,且
是
和
的等差中项.
(1)设
,求证:数列
为等比数列;
(2)若
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b2cc1095ffa20e537b02de51e2bc45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36dfab3d1da98786344a73a58bfb6b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331f96a1ebc7b11e8177c50c70c094a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62bae11b31f657478e97646895a289e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f379a3b2ecaa07bad3bbcd809d6b96.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ef7532d3061c9386aa9b2a4af65f2a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4f523bbf471c9811c1101cc76125a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f465a44170e765ed018eeca0d3054dc.png)
您最近一年使用:0次
3 . 设数列
的前
项和为
,且对于任意正整数
,都有
.
(1)求证:数列
是等比数列;
(2)设
,数列
的前
项和为
,求证:
.
![](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/ae734ad099abbb2f7efe7d7a6a4169fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6ae907495d2290796210e2ae99d711.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778f4a19ea50206683a9fbf1ebe4febe.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36925e53ab12172c7616b6d64b608b16.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9928e46511e601913619a427ded84a3.png)
您最近一年使用:0次
2023-12-26更新
|
1963次组卷
|
6卷引用:江苏省泰州中学、宿迁中学、宜兴中学2024届高三上学期12月调研测试数学试题
江苏省泰州中学、宿迁中学、宜兴中学2024届高三上学期12月调研测试数学试题2023-2024学年高二上学期期末数学仿真模拟试题03(新高考地区专用)江西省上饶市玉山县第二中学2024届高三上学期12月月考数学试题(已下线)专题04 数列通项与求和技巧总结(十大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)(已下线)重难点5-2 数列前n项和的求法(8题型+满分技巧+限时检测)(已下线)专题34 等比数列及其前n项和6种常见考法归类- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第二册)
解题方法
4 . 已知函数
.
(1)若
,求
的最小值;
(2)设数列
前
项和
,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c65664309a5af21b878b7720991fe10.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设数列
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5c8fc2f1b7e3dd6635e850d3d1ee1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd54a4949e7ead132cc159f98ccaca5.png)
您最近一年使用:0次
名校
解题方法
5 . 已知数列
的前
项和为
,且
,
.
(1)求数列
的通项公式;
(2)设
,数列
前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67fd0eb54561cd1df683a08cf049bfc.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/cec0e0155f66c9d8804482da899c20ea.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67fd0eb54561cd1df683a08cf049bfc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af49d87ac52004607e58bdac29297783.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa33d6f116c61ab89224c1a9886861cd.png)
您最近一年使用:0次
2023-10-21更新
|
3099次组卷
|
5卷引用:江苏省宿迁北附同文实验学校2023-2024学年高三上学期9月月考数学试题
江苏省宿迁北附同文实验学校2023-2024学年高三上学期9月月考数学试题河北省衡水市安平中学2023-2024学年高二上学期第三次月考数学试题广东省广州市第六中学2024届高三第二次调研数学试题河北省衡水市冀州中学2024届高三第一次调研数学试题(已下线)第09讲 第四章 数列 章节验收测评卷(综合卷)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)
2024·江苏连云港·模拟预测
6 . 已知数列
的前n项和为
,且
.
(1)证明:数列
是等差数列;
(2)数列
的每一项均为正数,
,数列
的前n项和为
,当
时,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0662a82b041a3a0450acd00b54c9fc48.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8dfb2af5bfd44046042a50e6edc1c4.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185fc63e4afb1a4f43c74e99549ff753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6339a180f3ac26326677a5f62c874ab.png)
您最近一年使用:0次
7 . 若数列
满足
,其中
,则称数列
为
数列.已知数列
为
数列,当
时.
(1)求证:数列
是等差数列,并写出数列
的通项公式;
(2)
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0af49723a69d6ae2e6dd5bf7704c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec574b71bbd7671223f8c833c8c8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec1a744042c32d0a851f98fafaa81f3.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05ea61581ab3ce0f51ec93f422143bd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0992722f5002aeafa39d25c6b5f4644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21085fbd6c4b34588f17fc466c845ffe.png)
您最近一年使用:0次
8 . 设数列
为等差数列,前
项和为
.
(1)求数列
的通项公式;
(2)设
的前
项和为
,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/1d70f81230f504b54007a05b64b72663.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d6968ee4cf919cea5d9bb309dfadc6.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/99b71dfb5c6c02fa99293d1e365ebc03.png)
您最近一年使用:0次
2024-05-11更新
|
674次组卷
|
3卷引用:江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题
江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题浙江省丽水市五校高中发展共同体2023-2024学年高二下学期5月期中考试数学试题(已下线)专题07 数列通项与数列求和常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
9 . 设等比数列
的前
项和为
,数列
为等差数列,且公差
,
.
(1)求数列
的通项公式以及前
项和
;
(2)数列
的前
项和为
,求证:
.
![](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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18883593a07bb08511c484b7af2af5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20379264b0b9a7d5c421bb23a1eb69fc.png)
(1)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)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f089de77d6fb7f086e899274d2f83a69.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/3ef2348f4e1af38c094221f82040337d.png)
您最近一年使用:0次
2023-09-21更新
|
941次组卷
|
4卷引用:专题09 数列求和6种常见考法归类(2)
(已下线)专题09 数列求和6种常见考法归类(2)河北省秦皇岛市青龙满族自治县2023届高三联考模拟(三)数学试题重庆市2024届高三上学期9月月度质量检测数学试题(已下线)专题5-3数列求和及综合大题归类-1
解题方法
10 . 已知等差数列
的首项为1,前
项和为
.记
,数列
是等差数列.
(1)求数列
的通项公式;
(2)设数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/f646ccf184a24c5398f0f630787e4fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e17fdf9be7e55937b98f746a6175d57.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/f1cb91e89800a81f4d62ed75c3ace24a.png)
您最近一年使用:0次