名校
1 . 对于有限数列
,如果
,则称数列
具有性质P.
(1)判断数列
和
是否具有性质
,并说明理由;
(2)求证:若数列
具有性质
,则对任意互不相等的
,有
;
(3)设数列
具有性质
,每一项均为整数,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbda012568d1b987d82212f259c224df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc2ea2a3ad08c9b500689edf05315c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3689290fc990f8750bef9a9c3217206e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2794054d69398d2ab71cd9d10249a820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)求证:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ac32d1c1245ecf6b501994a32084fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60051144e33707f6aa51b2fe09925268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb993b6e0950ed30054ab1f5b8939aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3151c7e71673e7e315492cdfa71d3808.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23856dd23f57468e9d82b1df395ae3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60051144e33707f6aa51b2fe09925268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f02970990111c4a3c87a5c8a223990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163d50dd737d0985fdba6d7d22d2ee94.png)
您最近一年使用:0次
2 . 已知数列
中,
,
.正项等比数列
的公比
,且满足
,
.
(1)证明数列
为等差数列,并求数列
和
的通项公式;
(2)如果
,求
的前n项和为
;
(3)若存在
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ac9d17bc8f166fc3894bf865ad6a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21cfd1ad0f4254be1d88c6577b6bbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90d19bcd582ed71cde0f18027174459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e3824ddd2210bd1e6313ad11dc8b13.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102abb18c888eb23d40708b97de140ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c39de50ed2f805d9c28aa7aadc46fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066141ba294715e4e725d59acfb85caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
3 . 设正整数
,其中对于任意
,
. 函数
满足
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06df740022c2c594bd0c069626e2cddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560d779b6110e79275749b1911a557f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5a20ff43995563aa4638efdf46359c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b8de661bf5d2d2ab1fa2bd97babb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092d08b0a38fd9bef76f7168ce1fc9dc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知各项均为正数的等差数列
与等比数列
满足
,又
、
、
成等比数列且
.
(1)求数列
、
的通项公式;
(2)将数列
、
的所有公共项从小到大排序构成数列
,试求数列
前2021项之和;
(3)若
,数列
是严格递增数列,求
的取值范围.
![](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/8592b997d19abf462dfa657056dea220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8c8586102d9ee54feafe54649b4b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e344c4b85a73ad4655a64b246f89bf54.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)将数列
![](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/5ed900c88cf1ca707255cd73398f6321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed900c88cf1ca707255cd73398f6321.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e538c13119bfa09ed8a2f15cd6ead3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
5 . 若数列
的前
项和为
,
,则称数列
是数列
的“均值数列”.已知数列
是数列
的“均值数列”且通项公式为
,设数列
的前
项和为
,若
对一切
恒成立,则实数
的取值范围为( )
![](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/9c4867dfd2b1fa71e386275fe0fed234.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6bf1602d6658253b63c98c5a0279e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-11-30更新
|
2155次组卷
|
13卷引用:四川省南充市白塔中学2020-2021学年高一下学期第二次月考(6月)数学试题
四川省南充市白塔中学2020-2021学年高一下学期第二次月考(6月)数学试题百校联盟2021届普通高中教育教学质量监测考试(全国新高考卷)数学试题(已下线)专题9 数列通项公式和前n项和-2021年高考冲刺之二轮专题精讲精析(已下线)“8+4+4”小题强化训练(32)数列的综合应用-2022届高考数学一轮复习(江苏等新高考地区专用)甘肃省会宁县第一中学2021-2022学年高二上学期期中考试数学(文)试题甘肃省会宁县第一中学2021-2022学年高二上学期期中考试数学(理)试题山东省烟台莱阳市第一中学2021-2022学年高二下学期开学摸底考试数学试题吉林省抚松县第一中学2021-2022学年高二下学期开学考试数学试题江苏省连云港市灌南高级中学2021-2022学年高二提优班上学期10月月考数学试题宁夏银川一中2023届高三上学期第三次月考数学(文)试题江苏省常州市第三中学2022-2023学年高二上学期期末数学试题河南省顶级名校2022-2023学年高三上学期1月阶段性检测文科数学试题江苏省南通西藏民族中学2022-2023学年高二上学期期中数学试题
11-12高三上·江苏泰州·期中
名校
6 . 设
是函数
的图象上任意两点,且
,已知点
的横坐标为
.
(1)求证:
点的纵坐标为定值;
(2)若
求
;
(3)已知
=
,其中
,
为数列
的前
项和,若
对一切
都成立,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cab3add12dd55b5ee45c2f31b24081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ac6a58d2abf245314865594db00b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37297dbe12721370c878bf5cbbd39ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb30d7ab63c72db80273ceab6a08e9e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2692d7d2bf71dac9313e2471d64a4cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471d81a803cd0db54214af321398c921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/75ad617393a9b09e0201bb54f9a58705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-10-20更新
|
1274次组卷
|
7卷引用:2014-2015学年四川省眉山市高一下学期期末考试数学试卷
2014-2015学年四川省眉山市高一下学期期末考试数学试卷江西省抚州市临川一中2018-2019学年高一下学期第二次月考数学试题四川省仁寿第一中学南校区2019-2020学年高一6月月考数学试题(已下线)2012届江苏省泰州中学高三上学期期中考试数学(已下线)专题07 数列与不等式相结合问题(第二篇)-备战2020年高考数学大题精做之解答题题型全覆盖(已下线)专题22数列求和方法的求解策略解题模板(已下线)专题11 数列前n项和的求法 微点2 倒序相加法求和
7 . 已知数列{an}满足条件an+1﹣an=2,a5=11,前n项和为Sn,数列{bn}前n项和为Tn,满足条件Tn=2bn﹣2.
(1)求an与bn;
(2)求数列{an•bn}的前n项和Kn;
(3)令Cn=
,若不等式x2+2mx+1≥C1+C2+C3+…+Cn对任意x∈R和任意的正整数n恒成立,求实数m的取值范围.
(1)求an与bn;
(2)求数列{an•bn}的前n项和Kn;
(3)令Cn=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfce215f34f701ee7c2cd2889a50f3f1.png)
您最近一年使用:0次
名校
解题方法
8 . 已知数列{an}满足
,若2≤a10≤3,则a1的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f42d684f722577b7772e0aee32d9fe.png)
A.1≤a1≤10 | B.1≤a1≤17 | C.2≤a1≤3 | D.2≤a1≤6 |
您最近一年使用:0次
2020-09-10更新
|
1019次组卷
|
11卷引用:新疆新源县2020-2021学年高一下学期期末联考数学试题
新疆新源县2020-2021学年高一下学期期末联考数学试题浙江省2019年6月普通高中学业水平考试数学试题1(已下线)浙江省2019年6月普通高中学业水平考试数学试题(已下线)第二章+数列(能力提升)-2020-2021学年高二数学单元测试定心卷(人教版必修5)(已下线)黄金卷03-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(江苏专用)(已下线)2021年高考数学押题预测卷(江苏专用)01陕西省咸阳市2021届高三五月数学信息专递试题(已下线)考点突破14 数列-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)(已下线)第4章《数列》 培优测试卷(二)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)陕西省延安市第一中学2022-2023学年高二上学期第一次月考文科数学试题安徽省合肥市第一中学2023-2024学年高二上学期素质拓展训练(10)数学试题
解题方法
9 . 已知数列
满足
.
(1)求数列
的通项;
(2)设
,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c811b8b0124c799580b5fa9cae3929.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980d51ba3340a31964fbec9e6f243ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcbc64b0f3d08d5285ee32e5ca13d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6afc5de00034c4b65e5c2841c1e299.png)
您最近一年使用:0次
10 . 已知等比数列
满足
,
,正项数列
前
项和为
,且
.
(1)求数列
和
的通项公式;
(2)令
,求数列
的前
项和
;
(3)若
,求对所有的正整数
都有
成立的
的范围.
![](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/d12da38ad96a3e687e0a0d7ee117c791.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ea1ef8209eefc99eecff0427369bb9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d6fbdd4ba14cb5192136175f4a13ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2020-07-25更新
|
1048次组卷
|
4卷引用:黑龙江省哈尔滨市第九中学2019-2020学年高一下学期数学月考试题
黑龙江省哈尔滨市第九中学2019-2020学年高一下学期数学月考试题黑龙江省哈尔滨市第九中学2019-2020学年高一下学期数学期末试题辽宁省营口第五中学2020-2021学年高三上学期第二次月考数学(理)试题(已下线)2021年新高考天津数学高考真题变式题16-20题