1 . 已知数列
:
的各项均为正整数,设集合
,记
的元素个数为
.
(1)若数列
:
,且
,
,求数列
和集合
;
(2)若
是递增的等差数列,求
的值(用
表示),并说明理由;
(3)请你判断
是否存在最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9ef2e730239fb441c867d6ab4d9b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f05a921b593d6e1bedfd6c28b60f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab8cdaf36beae93dd45c27981cb75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc668d959b811bef55a1e672eb1dcec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f255d89ed61b51eb161d74e518b9a763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(3)请你判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a318eb5a4da016d3d993175e845a90ab.png)
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2 . 我们称各项均不相等的正项数列
为“冒泡数列”,对任意冒泡数列,我们按如下步骤进行操作,称为“冒泡操作”
比较
的大小,若
,则交换
的位置;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,若
,再交换
;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,
,直到比较得到
时或者
调整位置至首位时停止比较和交换位置,并进行下一步;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,…,直到比较得到
或者
调整位置至首位时结束操作.
(1)请对数列
5,3,2,9,7作冒泡操作,可表示为
请写出操作结束后得到的数列,并计算交换位置的次数.
(2)对于某个
项冒泡数列
当其完成冒泡操作时的总的交换位置的次数称为其“交换复杂度”,记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a802b2e8db56dfb2f367fbbd9c4fe0f.png)
(i)求
的最小值和最大值;
(ii)对于某个
项冒泡数列
及其各项全排列产生的所有不同数列,其交换复杂度的平均数记为
,求
的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8e9680996fdd9e3a40f62d810e92e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa559d2ca921738d0c6c51f3a036880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ade3a1d01605706801e238726e55fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cfe1386cf3dae99d19bf57895c9f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a25a0b38f47e113fd4dd76832de690a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fee2a3f8c67509707271a3f266a8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8784badc8cc600bef381da22d1c628d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fee2a3f8c67509707271a3f266a8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0525db7ca68c21dfe7a1c4b543b4bee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9017d3641140e0692048ddbab24d1d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0525db7ca68c21dfe7a1c4b543b4bee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5356eacad97dae1c7e865903171245ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee15a08d7dc7c77ea81607b1f214c092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebefe3e26bef1c8422bfe5a472e0d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bc971d069730aa97e8734fc884e3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebefe3e26bef1c8422bfe5a472e0d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240e1ed0392e64705738776ff88b1623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0d398803d6a57b99fbb7994edc767b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed3a0a9f46932f86611d64711d81c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cace8ff9678eca7c3386f280c4ed8c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a67cfcf87e8b88246d7c8e101041bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0be03feff9bfb3b2f45a34b6fc2578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a67cfcf87e8b88246d7c8e101041bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d151f7e01f394c4547e8065de1adb689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5aeba46b164eea610a02251cdbfba03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)请对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569675dd7b2aca2732324f4bea5c02e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acd875285006bca9792d6ffbea60191.png)
(2)对于某个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be66b629b36c5fe55ff234ad59bffff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a802b2e8db56dfb2f367fbbd9c4fe0f.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94511620a0ee01ebcc8ac2f3a47ac87d.png)
(ii)对于某个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de53713b20a2f956c2590ce71fb69c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de53713b20a2f956c2590ce71fb69c37.png)
您最近一年使用:0次
名校
解题方法
3 . 如果数列
满足:
且
,则称数列
为
阶“归化数列”.若数列
还满足:数列
项数有限为
;则称数列
为“
阶可控摇摆数列”.
(1)若某6阶“归化数列”
是等比数列,写出该数列的各项;
(2)若某13阶“归化数列”
是等差数列,求该数列的通项公式;
(3)已知数列
为“
阶可控摇摆数列”,且存在
,使得
,探究:数列
能否为“
阶可控摇摆数列”,若能,请给出证明过程;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa0fca4198a6d5c5b76e5e1716dc4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112acfb7931e94ce87fa2b388316f2ed.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若某6阶“归化数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若某13阶“归化数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca8076f0553088afded57b48009d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb8fda29ceaba5063edb112d39b10f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
4 . “
序列”在通信技术中有着重要应用,该序列中的数取值于
或1.设
是一个有限“
序列”,
表示把
中每个
都变为
,每个0都变为
,每个1都变为0,1,得到新的有序实数组.例如:
,则
.定义
,
,若
中1的个数记为
,则
的前10项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeedb00753e7cf6d2631244ce112019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c928060da9aa0d459ca27a9e26d656cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeedb00753e7cf6d2631244ce112019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60a47fe3db1924469eb3c03f9073bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c928060da9aa0d459ca27a9e26d656cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02d9f149c12ef612345a0617650215e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bada33e0bb409c2b7c75f84b61c0864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28dc832f1e9e421ac03f848ac22eb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32ccd28d1aaf22369edb601d07c76ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8e99a137748fac22a827de8dae1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fd6f1e91e0d10c3b2421b59020f90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
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名校
5 . 已知数列
的通项为
,前
项和为
,则下列选项中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.如果![]() ![]() ![]() ![]() |
B.如果![]() ![]() ![]() ![]() |
C.如果![]() ![]() ![]() ![]() |
D.如果![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-05-21更新
|
954次组卷
|
3卷引用:湖南省长沙市第一中学2024届高三下学期模拟试卷(二)数学试题
6 . 若数列
在某项之后的所有项均为一常数,则称
是“最终常数列”.已知对任意
,函数
和数列
满足
.
(1)当
时,证明:
是“最终常数列”;
(2)设数列
满足
,对任意正整数
.若方程
无实根,证明:
不是“最终常数列”的充要条件是:对任意正整数
,
;
(3)若
不是“最终常数列”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc6de641322c6aeb24e0bbd875e65b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980f4d5c5ec0f551d7a3c3c0b5ffdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b26218ecae19cc13017d561c01d69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36737370e7f4231ebdd27c957f47f45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8f2cc86844dc647bfb33344781e75a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c77ea288be5bfb4445a76a2429aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
7 . 已知数列1,1,2,1,2,4,1,2,4,8,1,2,4,8,16,…,其中第一项是
,接下来的两项是
,
,再接下来的三项是
,
,
,依此类推.设该数列的前
项和为
,规定:若
,使得
,则称
为该数列的“佳幂数”.
(1)将该数列的“佳幂数”从小到大排列,直接写出前4个“佳幂数”;
(2)试判断50是否为“佳幂数”,并说明理由;
(3)(ⅰ)求满足
的最小的“佳幂数”
;
(ⅱ)证明:该数列的“佳幂数”有无数个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c187044e689bbe78aededb6b48f877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78697a69758b8d469a74236859514a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ad4668cc927e277289b2af718f0d91.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/0e32aebf990481784567d2e0ffe0bfeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6fd61f9687bd38555b5b3311d02c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)将该数列的“佳幂数”从小到大排列,直接写出前4个“佳幂数”;
(2)试判断50是否为“佳幂数”,并说明理由;
(3)(ⅰ)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619b65a1dbef822d8c5b6faeda865514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(ⅱ)证明:该数列的“佳幂数”有无数个.
您最近一年使用:0次
8 . 已知
为非零常数,
,若对
,则称数列
为
数列.
(1)证明:
数列是递增数列,但不是等比数列;
(2)设
,若
为
数列,证明:
;
(3)若
为
数列,证明:
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4fb301b1cc7b26989dc0155265ce8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5882782c03bbca5ac2140b17224139b9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15aa2314541715f6be69251653ebf6da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446e8a7985d4d3dd95c70dc4aad67861.png)
您最近一年使用:0次
2024-04-06更新
|
1120次组卷
|
3卷引用:湖南师范大学附属中学2023-2024学年高三下学期第一次模拟数学试卷
名校
9 . 超越数得名于欧拉,它的存在是法国数学家刘维尔(Joseph Liouville)最早证明的.一个超越数不是任何一个如下形式的整系数多项式方程的根:
(
,
,…,
,
).数学家证明了自然对数的底数e与圆周率
是超越数.回答下列问题:
已知函数
(
)只有一个正零点.
(1)求数列
的通项公式;
(2)(ⅰ)构造整系数方程
,证明:若
,则
为有理数当且仅当
.
(ⅱ)数列
中是否存在不同的三项构成等比数列?若存在,求出这三项的值;否则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc2287a601b334908c58609a5ce2f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf1336dd233a8630e7266f0a83dea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b3c450d9e72a71e5d2562c48e7cb6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)(ⅰ)构造整系数方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1641897cacc61faed30907970d1fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5dd1562138ab60802c33a17a8d7867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d835c32139c51bc210b9714048fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
(ⅱ)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2024-04-01更新
|
889次组卷
|
2卷引用:湖南省部分学校2024届高三下学期一起考大联考模拟(二)数学试题
名校
解题方法
10 . 已知数列
的前
项和为
,满足
;数列
满足
,其中
.
(1)求数列
的通项公式;
(2)对于给定的正整数
,在
和
之间插入
个数
,使
,
成等差数列.
(i)求
;
(ii)是否存在正整数
,使得
恰好是数列
或
中的项?若存在,求出所有满足条件的
的值;若不存在,说明理由.
![](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/83fd67e206753eff52406291c19daa38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23f7f601ad9971d3de3e2dd820642e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0197eeeeaafec6b1fdd7bb8509572f6b.png)
(2)对于给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd6f136f7c8d27b406c0993dcfece54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417083c7157cf0b45befc7c537f1012c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629e172f62f389ea84b7d771c1c27566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a039f1df440117fe89030a4ad6dcf291.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22be6bbf70b5c135edaf8db69118cb50.png)
(ii)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75ed0812322ed46d25ec41f609674be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-03-19更新
|
2002次组卷
|
6卷引用:湖南省九校联盟2024届高三下学期第二次联考数学试题