解题方法
1 . 已知数列
是无穷数列.若
,则称
为数列
的1阶差数列;若
,则称数列
为数列
的2阶差数列;以此类推,可得出数列
的
阶差数列,其中
.
(1)若数列
的通项公式为
,求数列
的2阶差数列的通项公式;
(2)若数列
的首项为1,其一阶差数列
的通项公式为
,求数列
的通项公式;
(3)若数列
的通项公式为
,写出数列
的
阶差数列的通项公式,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5653b60d16ec4e653518f0562680250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703cdc7668aa4dcab77e448249f9446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28182f211c5a2647e5963f94b7e39615.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dd3ce757a2ad080ece0e34424fb05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若数列
![](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/42fef6975d285cabcf6be67c78f30d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7614e7ffdeb8b48c6aaf660c4fef3e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
2 . 已知数列
. 若存在
,使得
为递减数列,则
称为“
型数列”.
(1)是否存在
使得有穷数列
为
型数列?若是,写出
的一个值;否则,说明理由;
(2)已知2022项的数列
中,
(
). 求使得
为
型数列的实数
的取值范围;
(3)已知存在唯一的
,使得无穷数列
是
型数列. 证明:存在递增的无穷正整数列
,使得
为递增数列,
为递减数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30f366b7d87e5e748367ac0a9df554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ad05e306652c42534c41636f5942ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30f366b7d87e5e748367ac0a9df554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fb9c93285f73ce392c6b8d3b2a8f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知2022项的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a55e4115c36490a40f83d15f066bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e306979e87a3cd19b2f390d374956f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a401c6c57a4aa884504b7a20a75b026a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a55e4115c36490a40f83d15f066bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)已知存在唯一的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30f366b7d87e5e748367ac0a9df554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bdb46e94cc0d92ebb508eec108ba531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbcb218505bec13380c6a2d730dd39c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d0ec71294e306ec78aac52f6753174.png)
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2022-06-23更新
|
589次组卷
|
4卷引用:专题06数列必考题型分类训练-3
3 . 若数列
同时满足下列两个条件,则称数列
具有“性质A”.
①
(
);②存在实数
,使得对任意
,有
成立.
(1)设
,试判断
是否具有“性质A”;
(2)设递增的等比数列
的前n项和为
,若
,证明:数列
具有“性质A”,并求出A的取值范围;
(3)设数列
的通项公式
,若数列
具有“性质A”,其满足条件的A的最大值
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e772be971634dc7230df59d91399dc59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670d5fc71b49fdb5411b046bb9a81bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c46b33730f3a29b9ec3024df71375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b39b97c1f6007e458646cf2655a0974.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a234044b6e65e53f5f0d979886be4f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942ed174dfdafaf5f0a68cac579110f8.png)
(2)设递增的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe308769d98da3757d3d3c9019ea84e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325bb1f4a88ca4e5bed08b5a4ede97ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f27f0c9be9710c55ab8e8d2cb4e56df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-06-23更新
|
625次组卷
|
4卷引用:专题06数列必考题型分类训练-3
4 . 对于无穷数列
、
,
,若
,则称数列
是数列
的“收缩数列”,其中
、
分别表示
中的最大项和最小项.
(1)写出数列
的“收缩数列”;
(2)证明:数列
的“收缩数列”仍是
.
![](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/02700430e0696cf6ada8c6fef8b98eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d20283237d19031ff2faaf77a10814.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/f8424af9108fc00fbf86a3d5c9409e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689a822a0d8b276fbe8596a2f94f7022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dd42e4f493477fb0f36137893d4d06.png)
(1)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dee512e0fdb19fc03858ce717ce8b7.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2022-06-12更新
|
208次组卷
|
3卷引用:北京第十二中学2021-2022学年高二6月份阶段性测试数学试题
名校
解题方法
5 . 已知数列
满足
,且
.
(1)求数列
的通项公式;
(2)已知数列
满足
,定义使
为整数的
叫做“幸福数”,求区间
内所有“幸福数"的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555d61c8244f57eda66297d8ef51bc7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f2e965ad7ab70a88d64a93307c1ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201edea14d2515226f5bc526b52054b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77707636638cd40540900577d89dc78.png)
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6 . 对于数列
,记
.
(1)若数列
通项公式为:
,求
;
(2)若数列
满足:
,
,且
,求证:
的充分必要条件是
;
(3)已知
,若
,
.求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c5f9b7b115d33b3ccbd3df5fc86a09.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b3dc0080aaf7d618423b1923d2dd1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54394bf6ef11138a744ca1727302742b.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7426d777b5072f53c5cd23bc066948ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46df866a9473cd08f37c276a5185a10b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b89e64dbabe7b186af978bcbfeadbe.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa1ffdd527ef0beba0cab676e6c3f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef3b334e457945dc436cffd0c4b166b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8e8817093cc3e6224779adab01cf5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1b69c3bf36d3e240d6d46ad648043e.png)
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名校
解题方法
7 . 数列
满足条件:若存在正整数
和常数
,使得
对任意
恒成立,则称数列
具有性质
,也称为类周期
数列.
(1)判断数列
是否具有性质
并说明理由;
(2)数列
具有性质
,且
,前4项成等差,求
的前100项和;
(3)若数列
既是类周期2数列,也是类周期3数列,求证:
为等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c3bc751242a284ad7c87ada9c8ac42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774eb1bdf5f27314132987e1afe4b200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5cf9c12181dd8683944b2b30bf8e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe22e04ef887ed4ccfa3db29e386079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fb4fa3a35884bdec69c437ea56d3af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe22e04ef887ed4ccfa3db29e386079.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9a3ea5e76e165faeabfdbc9717c287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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解题方法
8 . 若数列
满足
,则称
为E数列.记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452f984578bac22ed2acd1c9f1ed09b4.png)
.
(1)写出一个满足
,且
的E数列
;
(2)若
,
,证明E数列
是递减数列的充要条件是
;
(3)对任意给定的整数
,是否存在首项为0的E数列
,使得
?如果存在,写出一个满足条件的E数列
;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835d2370ce5ce890eb76763f4b5b8682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3578d2a4f7b670a9c555e35653baa1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452f984578bac22ed2acd1c9f1ed09b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2779f85ee54baca87c41e508633a705.png)
(1)写出一个满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2750dc9a0ad9b327da7a92f524cb90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2727681733ed1c0eeedacbcad8ab1a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52628090e3bc9a731b2310cae63a6b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c7867969b14fd642147188b6ebf29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fd15570bcd1cc1228fd3929a7c3f42.png)
(3)对任意给定的整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f27f84764f1cca89ce3d93fc1cf603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89726ddaa0e0b461bebe2efc831b0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次
名校
9 . 设正整数数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fcec9111f2e905229ace48be2ca6f.png)
.
(1)若
,请写出
所有可能的取值;
(2)记集合
,证明:若集合
存在一个元素是3的倍数,则
的所有元素都是3的倍数;
(3)若
为周期数列,求
所有可能的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fcec9111f2e905229ace48be2ca6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34434a0b7330efb26ef92e8e86301fd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d8c8d85bc63a7fca39acb0442ff167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(2)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21550abb7c545b53cd2336a7a76885fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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2022-04-14更新
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6卷引用:专题04 数列(5)
(已下线)专题04 数列(5)北京市顺义区2022届高三第二次统练数学试题北京市一零一中学2022届高三下学期三模数学试题(已下线)考点15 数列综合问题-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)北京一零一中学2023届高三下学期开学考数学试题(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
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10 . 设数列
.如果
,且当
时,
,则称数列A具有性质
.对于具有性质
的数列A,定义数列
,其中
.
(1)对
,写出所有具有性质
的数列A;
(2)对数列
,其中
,证明:存在具有性质
的数列A,使得
与
为同一个数列;
(3)对具有性质
的数列A,若
且数列
满足
,证明:这样的数列A有偶数个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65a1fd37e986a6657263d566fb2cb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f73d7a8c77f88995a3c89492b53b67de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4915d8f9706190d4d0b14aa42c2c7367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e2e9b1c158c5d4e2a1a2e1737013a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e8ef85162d03adbe3a2a6b7b19623.png)
(1)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fcf8639f59fb0ef4f9f6f6d0943a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57314e95aa54ed318c5fed57bc6d93fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1573d16b04edc29edf1340c9da13954c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40451e0f90ba4df0cb35143b93303a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(3)对具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e533e28452c0a087f29194aeb081523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40451e0f90ba4df0cb35143b93303a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0a22166c3eea2f12145d1906289a5a.png)
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8卷引用:北京市第八十中学2022-2023学年高二上学期适应性考试数学试题