名校
解题方法
1 . 在数列
中,若
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44656fcd82f07709972eb622cc463ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4a13bd477c3e49fee39ee687d6323cb.png)
您最近一年使用:0次
2024-03-06更新
|
476次组卷
|
2卷引用:北京市第九中学2023-2024学年高二下学期4月月考数学试卷
解题方法
2 . 数列
的通项公式为
则该数列第 10项为_______ ,其前10 项和为______ .(数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac286124905593c230dbcf127f361180.png)
您最近一年使用:0次
3 . 记无穷数列
的前n项中最大值为
,最小值为
,令
.
(1)若
,请写出
的值;
(2)求证:“数列
是递增的等差数列”是“数列
是递增的等差数列”的充要条件;
(3)若
,求证:存在
,使得
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293570f1284f5161d0c9e83c1aef7777.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d207b73fd6b888db038e3e0d17383958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447e5baee4f7518706498d4aca7553b.png)
(2)求证:“数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95a1e259bc8ae8f932a8743d63fc37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49684a3fb6e58fe4471f000528353656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac212ee4717d64901197c1a0a734f60.png)
您最近一年使用:0次
2023-03-26更新
|
483次组卷
|
2卷引用:北京市清华附中2023届高三下学期3月调研数学试题
名校
4 . 已知数列
.设集合
,如果对任意的整数
都有集合
的元素个数等于
,则称
为“完美数列”
(1)分别判断数列
和
是否为“完美数列”,直接写出结论:
(2)若
是“完美数列”,求证:
;
(3)若
是“完美数列”,且
,求出所有满足条件的数列
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d40f91eea8519183dae6bf2af64381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3102d97b673a8c708dde3b6ffbbe2138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c315caff37ae1ebfa412b2adfe130ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)分别判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308f9a69923d8f7347ce5af0fbdb3fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a033921506239df65e3296b1880c7e2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/273073906bb7091463fc477b774d49f0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33307fa505efcb8513ef6b6ac45624ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
解题方法
5 . 若数列
的通项公式是
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7405f8af1ab6ae282350762c167edcc4.png)
A.108是数列![]() | B.数列![]() |
C.前![]() | D.前![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知项数为
的数列
是各项均为非负实数的递增数列.若对任意的
,
(
),
与
至少有一个是数列
中的项,则称数列
具有性质
.
(1)判断数列
,
,
,
是否具有性质
,并说明理由;
(2)设数列
具有性质
,求证:
;
(3)若数列
具有性质
,且
不是等差数列,求项数
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc35d18037c40fec3a643a8a0ee1475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208dfb2f585802ed32c822b6a4005e83.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/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f784bc10c59038901c3183b43caccf85.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b170391de8265fab2b1ebae0f64faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2022-01-16更新
|
799次组卷
|
3卷引用:北京市第十七中学2024届高三上学期10月月考数学试题
北京市第十七中学2024届高三上学期10月月考数学试题北京市朝阳区2021-2022学年高二上学期期末数学试题(已下线)高二数学下学期期末精选50题(压轴版)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)
7 . 已知{an}是由正整数组成的无穷数列,该数列前n项的最大值记为An,最小值记为Bn,令
.
(Ⅰ)若an=2n(n=1,2,3,…),写出b1,b2,b3的值;
(Ⅱ)证明:bn+1≥bn(n=1,2,3,⋅⋅⋅);
(Ⅲ)若{bn}是等比数列,证明:存在正整数n0,当n≥n0时,an,an+1,an+2,…是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9813e4048d837b675e13a70cc3ad0e.png)
(Ⅰ)若an=2n(n=1,2,3,…),写出b1,b2,b3的值;
(Ⅱ)证明:bn+1≥bn(n=1,2,3,⋅⋅⋅);
(Ⅲ)若{bn}是等比数列,证明:存在正整数n0,当n≥n0时,an,an+1,an+2,…是等比数列.
您最近一年使用:0次
2021-09-05更新
|
320次组卷
|
7卷引用:北京市东北师范大学附属中学朝阳学校2023-2024学年高二上学期第三次月考数学试题
名校
8 . 已知数列
的通项公式是
,则220是这个数列的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df86feea976eda76181eb248a8b94eb6.png)
A.第19项 | B.第20项 | C.第21项 | D.第22项 |
您最近一年使用:0次
2020-06-04更新
|
427次组卷
|
4卷引用:北京市第三十五中学2021-2022学年高二6月月考数学试题
北京市第三十五中学2021-2022学年高二6月月考数学试题陕西省兴平市南郊高级中学2023-2024学年高二上学期第三次质量检测数学试题四川省仁寿第二中学、华兴中学2019-2020学年高一5月联考(期中)数学试题(已下线)4.1 数列的概念(精练)-2020-2021学年一隅三反系列之高二数学新教材选择性必修第二册(人教A版)
名校
解题方法
9 . 已知由n(n∈N*)个正整数构成的集合A={a1,a2,…,an}(a1<a2<…<an,n≥3),记SA=a1+a2+…+an,对于任意不大于SA的正整数m,均存在集合A的一个子集,使得该子集的所有元素之和等于m.
(1)求a1,a2的值;
(2)求证:“a1,a2,…,an成等差数列”的充要条件是“
”;
(3)若SA=2020,求n的最小值,并指出n取最小值时an的最大值.
(1)求a1,a2的值;
(2)求证:“a1,a2,…,an成等差数列”的充要条件是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858c881d66b4f60b16eb1b6339fed55f.png)
(3)若SA=2020,求n的最小值,并指出n取最小值时an的最大值.
您最近一年使用:0次
2020-05-10更新
|
663次组卷
|
3卷引用:2020届北京市第八中学高三下学期自主测试(二)数学试题
名校
解题方法
10 . 对于数列
,如果存在正整数
,使得
对一切
,
都成立,则称数列
为
等差数列.
(1)若数列
为2-等差数列,且前四项分别为2,-1,4,-3,求
的值;
(2)若
既是2-等差数列,又是3-等差数列,证明:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668a397301141b4e3fa8109515847004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52eecd38954cd0ca3fb26328a39bb859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85236e977c6de86166b422b0c6e6b91a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
您最近一年使用:0次