名校
解题方法
1 . 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.![]() |
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名校
解题方法
2 . 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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3 . 数列
的前n项之和为
,
,
(p为常数)
(1)当
时,求数列
的前n项之和;
(2)当
时,求证数列
是等比数列.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6a7e488682c7b7eabfc99031bd193.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194b8ab194c7d299d5c3e0f09ec18384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
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4 . 已知
是等差数列
的前
项和,
,设
,则数列
的前
项和为
,则下列结论中不正确的是( )
![](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/18442d8a4725e976728d591a6dcbf7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230ae9538a1b0ec62c3491cbce25df8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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5 . 已知数列
的通项公式为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71fcd5e5a26fa80c0a8372dfa80e79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5e622bc8bb294954a5c1a9a131bdfb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-04-20更新
|
2181次组卷
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7卷引用:江西省兴国县第三中学2020-2021学年高一下学期期中考试数学(兴特班)试题
江西省兴国县第三中学2020-2021学年高一下学期期中考试数学(兴特班)试题河北省石家庄市2021届高三下学期质检一数学试题(已下线)押第6题 数列-备战2021年高考数学(文)临考题号押题(全国卷2)陕西省西安市雁塔区第二中学2021-2022学年高一下学期第二次月考数学试题 (已下线)专题7.9 数列的函数性质—单调性与周期性(小题)-2022届高三数学一轮复习精讲精练(已下线)第16题 数列求和-2021年高考数学真题逐题揭秘与以例及类(新高考全国Ⅰ卷)(已下线)第43讲 数列的求和
名校
解题方法
6 . 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.![]() |
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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(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)“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)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
名校
解题方法
7 . 已知数列
满足
,
(
,
),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
(1)证明数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
为等比数列,求出
的通项公式;
(2)数列
的前项和为
,求证:对任意
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd675707e7b2a293d35c2c2690c13c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d307ec71820b6536453fbdb5069da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3860c78a8d25ac6b5c1cff5ebbd960fc.png)
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2020-11-07更新
|
1083次组卷
|
9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【全国百强校】河北省唐山市第一中学2019届高三下学期冲刺(一)数学(理)试题【市级联考】安徽省合肥市2019届高三下学期四月临考冲刺卷数学(理)试题湖北省襄阳五中、夷陵中学、钟祥一中三校2020届高三下学期6月高考适应性考试理科数学试题宁夏银川一中2021届高三第三次月考数学(文)试题宁夏银川一中2021届高三第三次月考数学(理)试题湖北省荆州中学2020-2021学年高二上学期12月月考数学试题河南省周口市太康县第一高级中学2022-2023学年高二上学期第一次月考数学(文科)试题 河南省周口市太康县第一高级中学2022-2023学年高二上学期第一次月考数学(理科)试题
名校
8 . 已知等差数列
的公差d大于0,且满足
,
.数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17a247427fce812293328a089457c03.png)
.
(1)求数列
,
的通项公式;
(2)设
,求
取得最大值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f5f3cf1a6b833876d99527f41c8107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0997f872e498cb3db3198a824d694c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17a247427fce812293328a089457c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4af9b6fb8da12989e3d6c8c3e15b8.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703a0fbc6e6abb249602e099dcad414f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2020-10-27更新
|
408次组卷
|
2卷引用:四川省雅安市雨城区雅安中学2020-2021学年高一下学期4月月考数学试题
名校
解题方法
9 . 已知等差数列
满足
,
,数列
满足
,记数列
的前n项和为
,若对于任意的
,
,不等式
恒成立,则实数t的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11dc2142789b4453e8c095b44e31545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154e9508f7a24a97d694e778452d2eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10dd628a48cf11a09a49d38b40d1ce26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3317d073fefd5aebc4ec26bc2697518.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-10-18更新
|
757次组卷
|
5卷引用:江西省南城一中2020-2021学年高一4月月考数学(理)试题
江西省南城一中2020-2021学年高一4月月考数学(理)试题重庆市第一中学2019-2020学年高一下学期期中数学试题(已下线)考点31 等差数列的概念、通项公式与求和公式应用(考点专练)-备战2021年新高考数学一轮复习考点微专题(已下线)考点33 数列求和(考点专练)-备战2021年新高考数学一轮复习考点微专题江西省新余市2021-2022学年高二上学期期末数学(文)试题
10 . 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)
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