1 . 已知数列
的前
项和为
,把满足条件
(对任意的
)的所有数列
构成的集合记为
.
(1)若数列
的通项为
,判断
是否属于
,并说明理由;
(2)若数列
的通项为
,判断
是否属于
,并说明理由;
(3)若数列
是等差数列,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/772a40f2fe006d9f15c82eb3fd5b78a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3919cbdc2edbb3237d379f2b7eeb36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78a26e3eeac053424c52ab90f6a3490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6a0be735ff99ec17214e79fab3b8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
2020-06-25更新
|
319次组卷
|
3卷引用:2020届上海市长宁区高三三模数学试题
名校
解题方法
2 . 在平面直角坐标系中,定义
(
)为点
到点
的变换,我们把它称为点变换,已知
,
,
,
是经过点变换得到一组无穷点列,设
,则满足不等式
最小正整数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f6138fb762d7fca4c295153b716616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9979465ce76b8582067703b39a0bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a73f95353bb2782779c976a6b82737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42795469ed8ba12729fcebd710e8795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a4422395ca20fe847419ec569e48b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddbde5d269189fced4cc478908a6866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c5bbac2b16b461a28d350728aee67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595fd9d54ab549c3462bc7e2be8370a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.9 | B.10 | C.11 | D.12 |
您最近一年使用:0次
2020-06-13更新
|
1238次组卷
|
8卷引用:上海市建平中学2020届高三下学期6月月考数学试题
3 . 设由复数组成的数列
满足:对任意的
,都有
(
是虚数单位),则数列
的前2020项和的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6a71dce20a87b70907438836fce9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次
2020-06-12更新
|
501次组卷
|
6卷引用:上海市静安区2020届高三下学期6月教学质量检测数学试题
上海市静安区2020届高三下学期6月教学质量检测数学试题2020届上海市静安区高三第二次模拟数学试题湖北省黄石市第二中学2020-2021学年高三上学期10月测试数学试题上海市进才中学2022届高三下学期3月月考数学试题上海市实验学校2022届高三下学期5月月考数学试题(已下线)对点练39 等比数列及其前n项和-2020-2021年新高考高中数学一轮复习对点练
4 . 已知数列
和
满足
,
,
,
.
(1)证明:
是等比数列,
是等差数列;
(2)求
和
的通项公式;
(3)令
,求数列
的前
项和
的通项公式,并求数列
的最大值、最小值,并指出分别是第几项.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ea014220aa658c8baa6e1f43e686a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d24dc5049b3ecd0f4892c63aebe5176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36edb6320f76289e704f94642a48da4.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c394d7bd6be49f089aa78d2d4fd0a9cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa779be3036f072af225380d85f662f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1fa6b5644dd1b383f245f5a66cdf485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.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/ad83668ff336589f82a2cd04db9f9947.png)
您最近一年使用:0次
2020-06-04更新
|
461次组卷
|
4卷引用:上海市复旦附中2019-2020学年高一下学期5月测试数学试题
上海市复旦附中2019-2020学年高一下学期5月测试数学试题上海市复旦大学附属中学2019-2020学年高一下学期线上教学评估数学试题上海市杨浦区复旦附中2019-2020学年高一下学期期中数学试题(已下线)专题7.5 数列的综合应用(精练)-2021年新高考数学一轮复习学与练
5 .
是一个边长为1的正三角形,
是将该正三角形沿三边中点连线等分成四份后去掉中间一份的正三角形后所形成的图形,依次类推
是对
中所含有的所有正三角形都去掉中间一份(如图),记
为
的面积,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e346fc67bc995e73ddea613683910c5.png)
________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac014a8e56460b25941958a93282fd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46217887957b2153adf03f96052ad2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e346fc67bc995e73ddea613683910c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/57e0642c-5392-407b-9706-caf730687f40.png?resizew=488)
您最近一年使用:0次
2020-06-04更新
|
819次组卷
|
7卷引用:上海市复旦附中2019-2020学年高一下学期5月测试数学试题
上海市复旦附中2019-2020学年高一下学期5月测试数学试题上海市复旦大学附属中学2019-2020学年高一下学期线上教学评估数学试题上海市杨浦区复旦附中2019-2020学年高一下学期期中数学试题江苏省南通市启东中学2020届高三下学期高考预测卷(一)数学试题(已下线)押第13题 推理与证明-备战2021年高考数学(文)临考题号押题(全国卷2)(已下线)专题27 等差数列与等比数列问题的精彩妙解-备战2022年高考数学一轮复习一网打尽之重点难点突破(已下线)专题17 盘点数列与其它知识交汇问题——备战2022年高考数学二轮复习常考点专题突破
6 . 定义:
是无穷数列,若存在正整数k使得对任意
,均有
则称
是近似递增(减)数列,其中k叫近似递增(减)数列
的间隔数
(1)若
,
是不是近似递增数列,并说明理由
(2)已知数列
的通项公式为
,其前n项的和为
,若2是近似递增数列
的间隔数,求a的取值范围:
(3)已知
,证明
是近似递减数列,并且4是它的最小间隔数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5868622de607b54d53fc6c481dc6302d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd6e7277f682a7f7adf2243ac5c9e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b2c4b8c1ebc9a3622f7d09de41496f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73841553d9289a6463664c8ea4647127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2020-05-19更新
|
398次组卷
|
4卷引用:2020届上海市宝山区高三下学期二模数学试题
2020届上海市宝山区高三下学期二模数学试题(已下线)上海市华东师范大学第二附属中学2019-2020学年高一下学期期末数学试题上海市七宝中学2022届高三上学期十月月考数学试题上海市文建中学2022-2023学年高一上学期期中数学试题
名校
解题方法
7 . 设数列
对任意
都有
(其中
、
、
是常数) .
(Ⅰ)当
,
,
时,求
;
(Ⅱ)当
,
,
时,若
,
,求数列
的通项公式;
(Ⅲ)若数列
中任意(不同)两项之和仍是该数列中的一项,则称该数列是“封闭数列”.当
,
,
时,设
是数列
的前
项和,
,试问:是否存在这样的“封闭数列”,使得对任意
,都有
,且
.若存在,求数列
的首项
的所有取值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708ecce72c7002204dc114d8df4ef913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee4ee43bf33b641aadeba4dd939cfa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fe8fecffe2d718a9a346173e5f7e6e.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d9880afb9e2262dbfcf20235e85a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced4e381e8c3336848b8c436dbc584f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a77080abccc0503b2a90eec3a64e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅲ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d9880afb9e2262dbfcf20235e85a62.png)
![](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/1bf4000fec5bf94d56935108d72af3c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d236a265a6cc0f3d06a0e568ffa907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abda7bb44fd2ba0f5c8fe8ed957748f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
2020-04-08更新
|
239次组卷
|
4卷引用:上海市长宁区延安中学2017届高三上学期12月月考数学试题
上海市长宁区延安中学2017届高三上学期12月月考数学试题2020届北京市育英中学高三3月月考数学试题江苏省合作联盟学校2019-2020学年高三下学期阶段性调研测试数学试题(已下线)考向18 数列不等式-备战2022年高考数学一轮复习考点微专题(上海专用)
名校
解题方法
8 . 设正数数列
的前
项和为
,对于任意
,
是
和
的等差中项.
(1)求数列
的通项公式;
(2)设
,
是
的前
项和,是否存在常数
,对任意
,使
恒成立?若存在,求
取值范围;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5deda1cd6fa436beb194738f75ee1650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41851f114b7bf2f00e8d8c95e67c7a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c0c10f6efb455932e16b9a397692db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
9 . 从数列
中可以找出无限项构成一个新的等比数列
,使得该新数列的各项和为
,则此数列
的通项公式为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f58a312af2125e5a09586045ecae1e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1985174e05ad371e13cf24d244423da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
您最近一年使用:0次
解题方法
10 . 数列
是等比数列,
,
,且公比
为整数,则数列
的前
项和
的值为__________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/961c1b28170a1c0c0ea36593eb635dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f11d02c774e3a41bfe1621548b2b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次