解题方法
1 . 如果数列
满足:
且
,则称数列为“
阶万物数列”.
(1)若某“4阶万物数列”
是等比数列,求该数列的各项;
(2)若某“9阶万物数列”
是等差数列,求该数列的通项公式;
(3)若
为“
阶万物数列”,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def85ab2340cabdaf18d4ce634dc2382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a0786747620e2ddecc5358435158d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若某“4阶万物数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若某“9阶万物数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](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/890bac6a077220d5582db2a929b677f9.png)
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2 . 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)求
;
(2)若
,求n的最小值;
(3)是否存在实数
,使得数列
为等比数列?若存在,求出
满足的条件;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcd08431daac10be93e6fafbc5d4a90.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
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3 . 已知
是正项数列
的前
项积,且
,将数列
的第1项,第3项,第7项,…,第
项抽出来,按原顺序组成一个新数列
,令
,数列
的前
项和为
,且不等式
对
恒成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/0b126acb59207c1478f317fd5e188879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5214be4ab4c116b6d8beb768db721cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df57c4df55b1d63c5bfa330940a351ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.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/380ddfd4e5671a323aae3c7074b233ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
A.数列![]() | B.![]() |
C.![]() | D.实数![]() ![]() |
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|
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2卷引用:辽宁省朝阳市建平县高级中学2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
4 . 已知数列
的前
项和
满足
,记
,数列
的前
项和为
,且对任意的
恒成立,则( )
![](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/8a29f39b208abece91e5acf117723dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a21fa97e82bb67e263b94fa1612c157.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/32b89a80dbd80aaf5b6d25a914001320.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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|
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5 . 已知数列
的前
项和为
,
.
(1)求
的值;
(2)证明数列
是等比数列,并求出数列
的通项公式;
(3)数列
中是否存在三项,它们可以构成等差数列?(结论不要求证明).
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb6457669c73995424232d9ef67983b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e616142cd7122cb7c4e9bc46bb7394.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17d72d1d20d385920c3d9da6bed8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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6 . 设
为数列
的前n项和,若
,且存在
,
,则
的取值集合为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194463e3b011603ff59c0789bcb65c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d0919893474b813ff79a073cd69cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441f0c1f9853bc3104d1ff4cde2a79b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知点列
,其中
,
,
是线段
的中点,
是线段
的中点,……
是线段
的中点,…….记
,则.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
______ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292db1408ccce5ca3ac3f5e4bb233171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b6ab454199d2738ea1b5cefb133d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e5160ff110a19878e4fae639319e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11603c89c66f064b263af841dae023f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a4f2bafc3346d14a8967ce2546157d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c775fc62e7696028a9184e5212f0446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc875ca919921e8f63a6fca648561b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
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名校
解题方法
8 . 满足
的最小正整数
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a966f87c3c0797cc0402bdbf297cbbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.12 | B.13 | C.17 | D.18 |
您最近一年使用:0次
名校
9 . 在不大于
的正整数中,所有既不能被2整除也不能被3整除的数的个数记为
.
表示不超过x的最大整数,令
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c0ad2f70bc2e383d06e8bc88d0f5f7.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba7f2a81cd4d39999be37eabefdfa52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528abce3183f3c3d429e205db5310455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4718c184ea3a28368846d39729c1fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c0ad2f70bc2e383d06e8bc88d0f5f7.png)
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10 . 已知
为数列
的前
项和,数列
满足:
,
,记不超过
的最大整数为
,则
的值为( )
![](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/b6a24198bd04c29321ae5dc5a28fe421.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/20fda9415d094adf1f19135f1b59ecea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d5257ce85e0d4d21a8ec227722bd8e.png)
A.4 | B.3 | C.2 | D.1 |
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2024-05-30更新
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2卷引用:福建省莆田第四中学2023-2024学年高二下学期期中考试数学试卷