名校
解题方法
1 . 已知无穷数列A:
,
,…满足:①
,
,…
且
;②
,设
为
所能取到的最大值,并记数列
:
,
,….
(1)若数列A为等差数列且
,求其公差d;
(2)若
,求
的值;
(3)若
,
,求数列
的前100项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df437d00ab1fd773e9d8d8f378455f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a49997086be2e13a271a4a7b1d4c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f63f64193d72aca5e88a2ea51e5ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d00457e8d086f28ea1b24bd880c9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f766f204cf98d973ad5abe03b235e95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398ba56f5a708d2d85a02320e1a389d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8c641c42b6cd7f44c477bbe5761a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7488ed7332650aa2bc908edbd38c05e8.png)
(1)若数列A为等差数列且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7104dd8a81267b6c15ceedcefccfa20.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398ba56f5a708d2d85a02320e1a389d.png)
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4卷引用:上海交通大学附属中学闵行分校2022-2023学年高二下学期3月月考数学试题
上海交通大学附属中学闵行分校2022-2023学年高二下学期3月月考数学试题上海市交通大学附属中学2022-2023学年高二下学期3月卓越考试数学试题(已下线)4.4 数学归纳法(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)江苏省南京市2024届高三上学期零模考前押题数学试题
2 . 如果数列
对任意的
,
,则称
为“速增数列”.
(1)判断数列
是否为“速增数列”?说明理由;
(2)若数列
为“速增数列”.且任意项
,
,求正整数k的最大值;
(3)已知项数为
(
)的数列
是“速增数列”,且
的所有项的和等于k,若
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182fe1cf64e38922b9038c9b9e382996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a97e99f49ad1998d2858e1963aa45de.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64810519cca09d8bad1e5c0720b6f70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f83982f63b139f23ae3846d08d6b2a.png)
(3)已知项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5631bc01b998a4b3fabd9e131699dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7056da59c6a57d96dc6e8534bb7ef74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e977500c1266a37522635c441e3f860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a3aa5e30bd2ccac16959d046bb38f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e45c34402a86a8ae4af80196ea62ae0.png)
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9卷引用:上海市奉贤中学2022-2023学年高二下学期期中数学试题
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3 . 在一个有穷数列的每相邻两项之间插入这两项的和,形成新的数列,我们把这样的操作称为该数列的一次“和扩充”.如数列1,2第1次“和扩充”后得到数列1,3,2,第2次“和扩充”后得到数列1,4,3,5,2.设数列a,b,c经过第n次“和扩充”后所得数列的项数记为
,所有项的和记为
.
(1)若
,求
,
;
(2)设满足
的n的最小值为
,求
及
(其中[x]是指不超过x的最大整数,如
,
);
(3)是否存在实数a,b,c,使得数列{
}为等比数列?若存在,求
b,c满足的条件;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb179b52814cf68ce86201e14c1dcae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)设满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d9ec2496e67711ab849b0f8988cd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28ede5e4c703019a7250cb63503df94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe1e778c9e668594c42b77459328c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf031d0c50f5013e0a8469d1f609d81.png)
(3)是否存在实数a,b,c,使得数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9fbbd9c88736e500f5251f97b08452.png)
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6卷引用:江西省赣州市南康区唐江中学2022-2023学年高二下学期期中数学试题
4 . 已知有穷数列
满足
.给定正整数m,若存在正整数s,
,使得对任意的
,都有
,则称数列A是
连续等项数列.
(1)判断数列
是否为
连续等项数列?是否为
连续等项数列?说明理由;
(2)若项数为N的任意数列A都是
连续等项数列,求N的最小值;
(3)若数列
不是
连续等项数列,而数列
,数列
与数列
都是
连续等项数列,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34eed025534d0f091c2d74c3b221399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c480b602b36fcca24f4d7b3cd691a272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f333fb57a0005bc7f1ff387708a2189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e510df019a124eb34fd770378d01f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc8f1ac7688c19152f095a513471455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb654dbe976f077495105b21b7963d0f.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02d39eac560e4fe7da7203dd2399b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4815b8b7203fb465809b395153ea3340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92b46d50ecc7ea20c610d9b1217582e.png)
(2)若项数为N的任意数列A都是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2837786afdd7b9b8bc37823040d7dd64.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9cf32c546edca415652dfb42300455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92b46d50ecc7ea20c610d9b1217582e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472e3136305dd6ad09931d02e251adac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b86aba0eba124ec529a2f306cd420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f326e4ea0d934c9bb0168dd6a9bf38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92b46d50ecc7ea20c610d9b1217582e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58365ff21052f2f978c11844b002b933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334c46af837676ada9575630a48d60f.png)
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北京市顺义区第一中学2022-2023学年高二下学期3月月考数学试题(已下线)第4章 数列单元测试能力卷-2023-2024学年高二上学期数学人教A版(2019)选择性必修第二册北京市第二中学2023-2024学年高二下学期学段考试数学试卷北京市北京师范大学附属中学2023-2024学年高二下学期期中考试数学试题北京市朝阳区2023届高三一模数学试题专题12压轴题汇总(10、15、21题)专题07数列北京卷专题18数列(解答题)北京市西城区北京师范大学附属中学2023-2024学年高三下学期开学测试数学试题(已下线)重难点10 数列的通项、求和及综合应用【九大题型】浙江省嘉兴市平湖市当湖高级中学2024届高三下学期5月下旬适应性测试数学试题
5 . 已知数表
中的项
互不相同,且满足下列条件:
①
;
②
.
则称这样的数表
具有性质
.
(1)若数表
具有性质
,且
,写出所有满足条件的数表
,并求出
的值;
(2)对于具有性质
的数表
,当
取最大值时,求证:存在正整数
,使得
;
(3)对于具有性质
的数表
,当n为偶数时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed47dfcc453bcc034a4c4490161da91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f90d683ac488837f9f4f0d36cef32.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3a3806d5350d02e410b1c008deeb77.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53be326052e623a71b1e8bbdd9c6f31e.png)
则称这样的数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce9d40adaecd9741d39abc0b3690431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc0451ddb250fc0b16fb794652b6f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce9d40adaecd9741d39abc0b3690431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891f611bbc4558380467c4b4016092a9.png)
(2)对于具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae125a86cb3414cf27b3e5476e2dfb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df0e3592f57e9715f9ed56bfc98241f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d42cc575e90606d0fda516f1023c213.png)
(3)对于具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a29fef95ed54dcf5c653749f5e9d232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae125a86cb3414cf27b3e5476e2dfb0.png)
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11卷引用:上海市上海中学2023-2024学年高二上学期期末考试数学试题
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名校
6 . 已知数列
.设集合
,如果对任意的整数
都有集合
的元素个数等于
,则称
为“完美数列”
(1)分别判断数列
和
是否为“完美数列”,直接写出结论:
(2)若
是“完美数列”,求证:
;
(3)若
是“完美数列”,且
,求出所有满足条件的数列
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d40f91eea8519183dae6bf2af64381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3102d97b673a8c708dde3b6ffbbe2138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c315caff37ae1ebfa412b2adfe130ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)分别判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308f9a69923d8f7347ce5af0fbdb3fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a033921506239df65e3296b1880c7e2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273073906bb7091463fc477b774d49f0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33307fa505efcb8513ef6b6ac45624ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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名校
解题方法
7 . 若无穷数列
满足以下两个条件,则称该数列为
数列.
①
,当
时,
;
②若存在某一项
,则存在
,使得
(
且
).
(1)若
,写出所有
数列的前四项;
(2)若
,判断
数列是否为等差数列,请说明理由;
(3)在所有的
数列中,求满足
的
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
①
![](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/8ff2d243ad2dc2094c8b3ea5672cfebd.png)
②若存在某一项
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c3ab5a5109ec773eadecca155377a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188bbb34acf76a5c5aa35c7faf9ef7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d37541605dfedeb0c28921950e362d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24431f390ba671b4de0d6abaeb9cf476.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d9b27f78829b57da918aa20936a198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b967232e28ad0d453adc66676bdf8b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
(3)在所有的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8cd9b2d7084a9db3df313891d64d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-03-18更新
|
984次组卷
|
8卷引用:北京市第三十五中学2022-2023学年高二下学期期中测试数学试题
北京市第三十五中学2022-2023学年高二下学期期中测试数学试题单元测试B卷——第四章 数列北京市石景山区2023届高三一模数学试题专题12压轴题汇总(10、15、21题)专题07数列北京卷专题18数列(解答题)北京市人大附中石景山学校2024届高三上学期10月检测数学试题(已下线)北京市第四中学2024届高三上学期10月月考数学试题变式题16-21
8 . 对于每项均是正整数的数列
、
、
、
,定义变换
,
将数列
变换成数列
、
、
、
、
.对于每项均是非负整数的数列
、
、
、
,定义变换
,
将数列
各项从大到小排列,然后去掉所有为零的项,得到数列
;又定义
.设
是每项均为正整数的有穷数列,令
.
(1)如果数列
为
、
、
,写出数列
、
;
(2)对于每项均是正整数的有穷数列
,证明
;
(3)证明:对于任意给定的每项均为正整数的有穷数列
,存在正整数
,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb6959af15155ee039bcb9fa0eeddee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a95ce7fd8358c26962a9e8d524d687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978e2f7118d2bd305086ae03cc7dd683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614206299653e4111ac285f5375e34c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07812c89c11b5cb96c2eb573e681cbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17923637012a75a01f309379c1909c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f610650fae8e1f446b736e608061a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1365b5e1c0926d9e303e33586ee520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405b31b30a80182dba0527eb436264ee.png)
(1)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(2)对于每项均是正整数的有穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4a4656523b5985571edfdd09340639.png)
(3)证明:对于任意给定的每项均为正整数的有穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b6ba2966874d33da6b94662d7cb23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291de980856351b0dd6582f33ab4d288.png)
您最近一年使用:0次
2023-03-09更新
|
1089次组卷
|
5卷引用:专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)北京市平谷区2023届高三一模数学试题北京市陈经纶中学团结湖分校2023届高三零模数学试题专题12压轴题汇总(10、15、21题)(已下线)2023年北京高考数学真题变式题16-21
9 . 对于给定数列
,如果存在实常数
、
使得
对于任意
都成立,我们称数列
是“
类数列”.
(1)若
,
,
,数列
、
是否为“
类数列”?
(2)若数列
是“
类数列”,求证:数列
也是“
类数列”;
(3)若数列
满足
,
,
为常数.求数列
前2022项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5306f3f7463bfbe4fd492cabd187dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8ec7c40d08dc7dd59aac94daa713ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592be188a2e5abad7f28fd68731cd1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd16130f139c09f6bb5d9cf54da904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次
10 . 对于数列
,规定数列
为数列
的一阶差分数列,其中
.
的通项公式为
,数列
的前n项和为
.
①求
;
②记数列
的前n项和为
,数列
的前n项和为
,且
,求实数
的值.
(2)北宋数学家沈括对于上底有ab个,下底有cd个,共有n层的堆积物(堆积方式如图),提出可以用公式
求出物体的总数,这就是所谓的“隙积术”.试证明上述求和公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f9d7c0929c0b60ceba9d0b9b64c180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1cda6d780be24695fe149cd26465ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc532bd4d671e5ba062609b35eb03a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f9d7c0929c0b60ceba9d0b9b64c180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
②记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f510ad524c266160a89d9ed100a5ddda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab8a7e95d65fd5fcb3650297ec75a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed64fcb9f979b4024cd4f3cf24bef07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)北宋数学家沈括对于上底有ab个,下底有cd个,共有n层的堆积物(堆积方式如图),提出可以用公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ace50878e5840c90c433eb1a99ba28.png)
您最近一年使用:0次
2023-02-13更新
|
1085次组卷
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4卷引用:山东省济南市2022-2023学年高二下学期期末数学试题
山东省济南市2022-2023学年高二下学期期末数学试题福建省泉州市泉港区第一中学2023-2024学年高二上学期第二次月考数学试题(已下线)重组1 高二期末真题重组卷(山东卷)B提升卷(已下线)专题11 数列前n项和的求法 微点3 裂项相消法求和(一)