1 . 已知数列
满足
,
.
(1)证明:数列
为等比数列;
(2)在
与
之间插入
个数,使得这
个数组成公差为
的等差数列,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57bfc1f8772f31748bfdc280d0712fc0.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4792fd59c4ca11ff03dc32e367c3983f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d1ae060458f733025fc82f7c7b14f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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4卷引用:河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题
解题方法
2 . 已知数列
的各项都为正数,且其前
项和
.
(1)证明:
是等差数列,并求
;
(2)如果
,求数列
的前
项和
.
![](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/28237e10ec7133ec600fbd57ed2ec664.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4565e9a0c413851da65f5c44c7ba82a2.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)
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2卷引用:2024届河南省名校联盟考前模拟大联考三模数学试题
名校
解题方法
3 . 数列
满足
则称数列
为下凸数列.
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
,其中
,
分别是公比为
,
的两个正项等比数列,且
,证明:
是下凸数列且不是等比数列;
(3)若正项下凸数列的前
项和为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0bee75d4d83c0b76421fd87113e4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f67fc95a626251da11649acb5e1706f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c340d7d093dd4a275ffea4b87cd26827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7aa870e2f199d6c12264fc9be86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若正项下凸数列的前
![](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/0002f427eded1721f43d60dd0fd3ffe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd419dc0a6580ab97777b2cb8fd7cded.png)
您最近一年使用:0次
2024-06-12更新
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5卷引用:河南省鹤壁市高中2024届高三下学期高考适应性考试(二)数学试题
4 . 已知无穷数列
是首项为1,各项均为正整数的递增数列,集合
,若对于集合
中的元素
,数列
中存在不相同的项
,使得
,则称数列
具有性质
,记集合
数列
具有性质
.
(1)若数列
的通项公式为
,判断数列
是否具有性质
,若具有,写出集合
与集合
;
(2)已知数列
具有性质
且集合
中的最小元素为
.集合
小的最小元素为
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b1f76afde7e8136dde47433ea74bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82079a5446d448fb1bea730b968d7e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9652602f1d23494c53743efe03db6bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aceba302deb7b46d2058ede7f356f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0380d25c8bccf9b2abdb668fb1bc5400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f603312b00ec0115ae36344b52ca689b.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c689cdf9d348002587f42b2c26be55f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aceba302deb7b46d2058ede7f356f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aceba302deb7b46d2058ede7f356f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682cbe4cd0d5cf5beb79d3ab89a117f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997ba7c3da0821973b7f44d2ca07fcd1.png)
您最近一年使用:0次
解题方法
5 . 若数列
的项
的最大奇因数为
,则
叫做
的“滤净数列”.已知数列
满足
是
的滤净数列.
(1)求
的通项公式及
的值;
(2)若
,求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](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/39a0c8aadb625077291084aa12f84c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1584461988bf6fbfef8be64226255c3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88252e8d8eb03422273cea5067de02bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed900c88cf1ca707255cd73398f6321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3076ec6b824db9b9b8b2857219eee0e9.png)
您最近一年使用:0次
2024-04-25更新
|
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|
3卷引用:河南省青桐鸣联考2023-2024学年高二下学期3月月考数学试题
6 . 已知数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)若存在
,使得
成立,求实数
的取值范围.
![](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/4d87c84f22c0c8eccf0b62fc57d62500.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6c6098cd1d27cd8c8e387bc143d811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-04-05更新
|
2768次组卷
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6卷引用:河南省信阳市第一高级中学(华大新高考联盟)2024届高三4月教学质量测评数学试题
名校
7 . 已知数列
为有穷数列,且
,若数列
满足如下两个性质,则称数列
为m的k增数列:①
;②对于
,使得
的正整数对
有k个.
(1)写出所有4的1增数列;
(2)当
时,若存在m的6增数列,求m的最小值;
(3)若存在100的k增数列,求k的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c1ee4d7c3f69fdd5a250ab8862d114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9db29473c5e28422317559df73a1037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa768d0bb9bcf827b3e7310e35ef0fbf.png)
(1)写出所有4的1增数列;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
(3)若存在100的k增数列,求k的最大值.
您最近一年使用:0次
2024-03-27更新
|
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4卷引用:河南省郑州市2024届高三第二次质量预测数学试题
解题方法
8 . 已知数列
的前n项和为
,且
.
(1)求
;
(2)若
,记数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498c96b078ab1ded4bdda837f83a3450.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438591068dee340b57be6d3f2b7fc70e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11dee498fc0e363bc1e79a1ce52dcd92.png)
您最近一年使用:0次
9 . 在正项等差数列
中,
,
.
(1)求数列
的通项公式;
(2)记
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6dd3ced080282d295aa343387cdca52.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.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/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-11-25更新
|
1384次组卷
|
6卷引用:河南省周口市项城市5校2024届高三上学期11月联考数学试题
河南省周口市项城市5校2024届高三上学期11月联考数学试题河南省金科新未来2023-2024学年高三上学期11月联考数学试题河北省保定市唐县第一中学2024届高三上学期期中数学试题贵州省黔东南州九校2024届高三上学期11月月考数学试题(已下线)第四章 数列(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)陕西省榆林市神木市第四中学2023-2024学年高二下学期开学检测考试数学试题
解题方法
10 . 已知在数列
中,
和
为方程
的两根,且
.
(1)求
的通项公式;
(2)若对任意
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84c767b6444b0cb99de76ba5d3f3561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd71bc7e6668f90f259ad0b06dd60c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737435fd9709dd85919c322906913c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e6a85980364f83a8ca9b55bd205f80.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2874cef06fa363930adde22ca4f4535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-09-18更新
|
703次组卷
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4卷引用:河南省周口市无锡天一企业管理有限公司等2校2022-2023学年高二上学期12月阶段性测试(二)数学试题
河南省周口市无锡天一企业管理有限公司等2校2022-2023学年高二上学期12月阶段性测试(二)数学试题陕西省咸阳市乾县第二中学2022-2023学年高二上学期12月阶段性测试(二)数学试题(已下线)拓展三:数列与不等式 -【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)江苏省连云港市灌南高级中学2023-2024学年高三上学期第一次月考数学试题