名校
1 . 已知
是各项均为正整数的无穷递增数列,对于
,定义集合
,设
为集合
中的元素个数,若
时,规定
.
(1)若
,写出
及
的值;
(2)若数列
是等差数列,求数列
的通项公式;
(3)设集合
,求证:
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542b4acf7b25b750fbe7205fd179b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857369257ea1b23ef40ce7e3a0f058af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1202d58cd3ad66e7b23f01024566705b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc57d8a4f67a040435d8b206d3254bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6510d0816033afa001c130342bb7cda.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b54e4701d4cb8d0133ad2044a7e0f52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1479e28bf6a8cb64ec7df77cd295f99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a6a3d1be93cf6d16ee6e0ce0497f46.png)
您最近一年使用:0次
2024-01-21更新
|
1353次组卷
|
7卷引用:江苏省常州市华罗庚中学2024届高三下学期4月二模训练数学试卷
江苏省常州市华罗庚中学2024届高三下学期4月二模训练数学试卷北京市朝阳区2024届高三上学期期末数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)讲(已下线)2024年高考数学二轮复习测试卷(北京专用)(已下线)黄金卷01(2024新题型)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编广东省江门市开平市忠源纪念中学2024届高三下学期高考冲刺考试(一)数学试卷
2 . 已知数集
,其中
,且
,若对
,
与
两数中至少有一个属于
,则称数集
具有性质
.
(1)分别判断数集
与数集
是否具有性质
,说明理由;
(2)已知数集
具有性质
,判断数列
,
,…,
是否为等差数列,若是等差数列,请证明;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c1d125b49fe60bc9796cf7d72e9170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550e79a4d9c549c9e28bbf30f74e24d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1906b96e054c5e74d295b61149a36b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ef5ce9b1b2850e4a95e7c0ce44bac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7152dfaf58cc9ff3df8c3d1ac7c435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/d7da2f386b78cdf6489efaa2f5820d3e.png)
您最近一年使用:0次
解题方法
3 . 已知集合
,设
整除
或
整除
,令
表示集合
所含元素的个数.
(1)写出
的值;
(2)当
时,写出
的表达式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a00635c06b220de5202131f839c2b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2798141f432848c5db590fd2fbe89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d56623b978f339511e2adaeae2e9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0de67a5a63a0f53fe034bd24da39f0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831608f09609c37f757f5bfcd01253f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
4 . 已知等差数列
与等比数列
是非常数的实数列,设
.
(1)请举出一对数列
与
,使集合
中有三个元素;
(2)问集合
中最多有多少个元素?并证明你的结论;
![](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/9b45ed42bacc8c561a88b41d2db90a88.png)
(1)请举出一对数列
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
(2)问集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
5 . 已知数集
,其中
,且
,若对
(
),
与
两数中至少有一个属于
,则称数集
具有性质
.
(Ⅰ)分别判断数集
与数集
是否具有性质
,说明理由;
(Ⅱ)已知数集
具有性质
,判断数列
是否为等差数列,若是等差数列,请证明;若不是,请说明理由.
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/e1eb57f01605458d802012bb52295afd.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/57fd2d5dc7104869a34e39e3d262632b.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/cf34d047a9504ea9a91e37c2df65f6ba.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/da4657758e754433ba506ac9ba36e101.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/f9f625e2e8d8432f97979758d46b7b7d.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/746b9cacc50a46e8bdc90edd9f72c8b3.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/2934a6319c564e3dbe31614c27e48cc5.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/0bb4632474874f73bd7694bf9f15f58c.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/0bb4632474874f73bd7694bf9f15f58c.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/24cf49bfe8944b998b8ecd2a1b81d1ce.png)
(Ⅰ)分别判断数集
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/8bd0b4dbfc684f30ab7d97f4a65f8001.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/0ae52e6d7bb442118748325acf9b4170.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/24cf49bfe8944b998b8ecd2a1b81d1ce.png)
(Ⅱ)已知数集
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/a37c24d5e53146da99b77f15c5e53c26.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/24cf49bfe8944b998b8ecd2a1b81d1ce.png)
![](https://img.xkw.com/dksih/QBM/2013/4/26/1571198307270656/1571198313226240/STEM/96b2f74824ac465a891939ba6e6047f0.png)
您最近一年使用:0次
2016-12-03更新
|
460次组卷
|
3卷引用:2013届江苏省扬州中学高三下学期期中考试数学试卷