名校
1 . 已知数列
满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0ba7d763145df190287145b0604e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
您最近一年使用:0次
名校
解题方法
2 . 若数列
满足
,其中
,则称数列
为M数列.
(1)已知数列
为M数列,当
时.
(ⅰ)求证:数列
是等差数列,并写出数列
的通项公式;
(ⅱ)
,求
.
(2)若
是M数列
,且
,证明:存在正整数n.使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a07614926587f57bc5f341c4f97f4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec574b71bbd7671223f8c833c8c8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec1a744042c32d0a851f98fafaa81f3.png)
(ⅰ)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115da54f93de5e89d1e7f443fccb61f8.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0992722f5002aeafa39d25c6b5f4644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21085fbd6c4b34588f17fc466c845ffe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a789a9be1723bfbd38ae538a9f39dc1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446e8a7985d4d3dd95c70dc4aad67861.png)
您最近一年使用:0次
2024-03-25更新
|
1249次组卷
|
3卷引用:天津和平区2024届高三一模数学试题
3 . 如果数列
,其中
,对任意正整数
都有
,则称数列
为数列
的“接近数列”.已知数列
为数列
的“接近数列”.
(1)若
,求
的值;
(2)若数列
是等差数列,且公差为
,求证:数列
是等差数列;
(3)若数列
满足
,且
,记数列
的前
项和分别为
,试判断是否存在正整数
,使得
?若存在,请求出正整数
的最小值;若不存在,请说明理由.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56c975b8b3195cea6ef4b9949e5d0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78393519255d80cb3c118a0d71f15511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4719086a4e785f6b5fdb429a313ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f236264ae54f3d8dc03d55c5c9ff88c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c88ebbe7b0f9cd88640b979a874a5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102c6cfe2a85d4dc2450fd082d625f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225c18d9b2d3afe311a2639e3e366249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f50ac3b1d543e1a09eb9e84da4f5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478421b81927e435cbcf5acafa89efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadd9a2715f906b05ad3122c0b2201c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b324005c139eec61bb7b4db496f10e49.png)
您最近一年使用:0次
2024-03-21更新
|
1470次组卷
|
4卷引用:2024届辽宁省高三二模数学试题
2024届辽宁省高三二模数学试题河北省廊坊市香河县第一中学2023-2024学年高三下学期模拟考试数学试卷(已下线)压轴题05数列压轴题15题型汇总-1广东省深圳市深圳高级中学(集团)2024届高三下学期适应性考试数学试卷
名校
解题方法
4 . 设数列
的前
项之积为
,满足
(
),则
( )
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5949f4a2c72dc07dfb2ba182f674db4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2771c5f04582c545e0f9afc8a2cb9597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd21f4cb498101d26b4aaa2e1a6addc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-21更新
|
3398次组卷
|
7卷引用:四川省成都市石室中学2023-2024学年高二下学期四月月考数学试题
5 . 已知数列
满足
.
(1)证明:数列
为等差数列,并求数列
的通项公式;
(2)记数列
的前n项和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6f47abdb81386321b6d20126e2a74d.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2024-03-13更新
|
529次组卷
|
4卷引用:河北省石家庄精英中学2023-2024学年高二上学期期末数学试题
河北省石家庄精英中学2023-2024学年高二上学期期末数学试题(已下线)专题02等差数列及其前n项和7种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)(已下线)专题04数列求和的6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)(已下线)专题03等比数列及其前n项和6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
2024高三下·全国·专题练习
6 . 已知数列
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5057abbf6c1db60c15727eac8e9acdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
您最近一年使用:0次
2024高三下·全国·专题练习
7 . 已知
和
都是等差数列,
的公差为2,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d1e25c7bdf31ee5705b76324fbd32a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e888dd5d501706c6d41c67c3180800fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
您最近一年使用:0次
2024高三下·全国·专题练习
8 . 已知数列
满足
,
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c19d77e4ea297db374071443e6cf8ac.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34050343cc5eee63a6dd6767b3192a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314501f06c7e4bf3112fe41ecac7be68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c19d77e4ea297db374071443e6cf8ac.png)
您最近一年使用:0次
2024高三下·全国·专题练习
9 . 已知数列
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb7147e313f9d9f67d19ecb5f499c05.png)
______ .
![](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/23e5a9566bb42dca9030be3915456c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb7147e313f9d9f67d19ecb5f499c05.png)
您最近一年使用:0次
23-24高二下·全国·课前预习
解题方法
10 . 已知{an}满足
,
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424edbd0bfe737cbb80c87d3c17ff560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4775666a3fd90a5623efeac883aeec.png)
A.48 | B.96 |
C.120 | D.130 |
您最近一年使用:0次