1 . 数列,
满足
,
,则
的前
项之和等于( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知数列
满足
,
,则
的整数部分是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c286f0bf939f0ec7abed0d75f414c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76be5c87dd8e20829874220f35f45e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bd1b650ddd204fb8783ab1406f3c94.png)
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3 . 在等差数列
中,
.
(1)求
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a144ca0cc7b7fc8c97c53a8f89a2f205.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a869747f7bd0da90c21c6be24bb400.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
2024-02-17更新
|
1598次组卷
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5卷引用:黑龙江省大兴安岭实验中学(东校区)2023-2024学年高二下学期期初考试数学试题
名校
解题方法
4 . 已知定义域为
的偶函数
满足
,且当
时,
,若将方程
实数解的个数记为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c723f5db15166d60a643607732e51b.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7852a186f6207db185658e9e00ca0eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8bf2bee2543a0a78c5529873e38f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c723f5db15166d60a643607732e51b.png)
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解题方法
5 . 已知数列
的前n项之积为
,且满足
.
(1)求证:数列
是等差数列;
(2)若数列
的前n项和为
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ccbf3a2fb89fb27111e60b12f3d4c28.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98bf0b0f74f57aabb128a237f1f3f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e07e56ca8103af9b3afc688220be33.png)
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2023-07-28更新
|
672次组卷
|
3卷引用:黑龙江省齐齐哈尔市克东县第一中学等2校2022-2023学年高二下学期开学考试数学试题
6 . 如图甲是第七届国际数学教育大会(简称ICME-7)的会徽图案,其主体图案是由图乙的一连串直角三角形演化而成的.已知
,
,
,
,…为直角顶点,设这些直角三角形的周长从小到大组成的数列为
,令
,
为数列
的前n项和,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/2/8952025e-950d-401d-845b-4b39ce02d7e8.png?resizew=324)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7318284526d4af3416d9827bdadf2822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9200c9dd0fb3f5ac96aaf9c0dfab14a6.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/e655c3679558fb18831485f61b06416d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/2/8952025e-950d-401d-845b-4b39ce02d7e8.png?resizew=324)
A.6 | B.7 | C.8 | D.9 |
您最近一年使用:0次
2023-07-28更新
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174次组卷
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2卷引用:黑龙江省齐齐哈尔市克东县第一中学等2校2022-2023学年高二下学期开学考试数学试题
名校
解题方法
7 . 已知定义域为R的偶函数满足
,且当
时,
,若将方程
实数解的个数记为
,则
您最近一年使用:0次
2023-06-03更新
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614次组卷
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4卷引用:黑龙江省哈尔滨德强学校2024届高三上学期开学考试数学试题(二卷)
黑龙江省哈尔滨德强学校2024届高三上学期开学考试数学试题(二卷)辽宁省实验中学2023届高三第五次模拟数学试题云南省三校2023届高三数学联考试题(八)(已下线)模块二 专题6《数列》单元检测篇 B提升卷(人教A)
8 . 已知数列
的前n项和为
,数列
的前n项积为
,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73ed03f680afec6efb011e781620478.png)
.
(1)求证:
为等差数列;
(2)记
,求数列
的前2023项的和M.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9f62781325acddbe6f2008e23243ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73ed03f680afec6efb011e781620478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e07bf129b073f37b553fbca100172.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff2e3d203ae24186524df6488785197.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a2d09cfd3fe13fdcbf2d9bd92cade7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
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2023-06-02更新
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4卷引用:黑龙江省哈尔滨德强学校2024届高三上学期开学考试数学试题
黑龙江省哈尔滨德强学校2024届高三上学期开学考试数学试题湖南省长沙市第一中学2023届高三二模数学试题(已下线)专题11 数列前n项和的求法 微点5 裂项相消法求和(三)(已下线)第02讲 等差数列及其前n项和(十大题型)(讲义)-1
名校
解题方法
9 . 已知
为等差数列
的前n项和,
,
.
(1)求
的通项公式;
(2)若
,
的前n项和为
,证明:
.
![](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/d046ec9d9aaac508a16462f2980ca18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9651204c54475c2e8cda8d0a6eeba177.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.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/aa33d6f116c61ab89224c1a9886861cd.png)
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2023-03-18更新
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5卷引用:黑龙江省龙西北八校联合体2022-2023学年高三下学期开学考试数学试题
名校
解题方法
10 . 已知函数
,其中
,且
.
(1)当
时,求
;
(2)设
,
,记数列
的前
项和为
,求使得
恒成立的
的最小正整数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2521f895ef2d5da87eba0da4ae7e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b755aa1ae2f79ab8be59e6a5a261d750.png)
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3375d6df57aea1bb928013aa83f972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-08-05更新
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3卷引用:黑龙江省鹤岗市工农区鹤岗市第一中学2023-2024学年高三上学期开学数学试题