已知数列
的前
项和为
满足:
,
.
(1)求数列
的通项公式;
(2)若数列
满足
.
①求数列
的前
项和
;
②若
对于一切正整数
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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56de8f4df2cbd501c56927d5e56847f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea78d43b7660b7e5113305c1c9788f9e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413fd42df3a6f774638ce6c169eb65b6.png)
①求数列
![](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)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84da8f2722417f099efae2169e66d8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
更新时间:2021-09-17 16:32:27
|
相似题推荐
【推荐1】已知数列
与
满足
,
.
(1)若
,且
,求
的通项公式;
(2)设
的第
项是最大项,即
,求证:
的第
项是最大项;
(3)设
,
,求
的取值范围,使得
有最大值M与最小值m,且
.
![](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/c6ece8e9ffa8e174590cb9e0a9fab6e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227482b4ed6195c3b7cb185f06771113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e1f790fa01181e6f062d7a46a7f1495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54395be36a4e0746b555b3882b107a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102567d85845f45c5ded80e0a800e4e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3004e1f1dd62f14feaad18936dd7e1.png)
您最近一年使用:0次
【推荐2】已知递增数列{an}前n项和为Sn,且满足a1=3,4Sn﹣4n+1=an2,设bn
(n∈N*)且数列{bn}的前n项和为Tn
(Ⅰ)求证:数列{an}为等差数列;
(Ⅱ)若对任意的n∈N*,不等式λTn
n
•(﹣1)n+1恒成立,求实数λ的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50440b23115963817529e267f194166c.png)
(Ⅰ)求证:数列{an}为等差数列;
(Ⅱ)若对任意的n∈N*,不等式λTn
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145708a2cca54ecebb6001805a3eac69.png)
您最近一年使用:0次
【推荐1】已知数列
的前
项和为
,满足
(
).
(1)求证:
是等差数列;
(2)已知
,且数列
的前
项和为
,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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761296ed6cfc2dc2618ccbe7f5467e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1505d56f0b35fe7f2de1fe1888036e4c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179513ce80436471efbe1d9b31735f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb2927659fc5b2b6c5ce1d97786c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9f747b00b90c90ad56bbb1a0f695eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
解题方法
【推荐2】已知等差数列
的各项均为正数,且
.设
表示不大于
的最大整数(如
).
(1)试求数列
的通项;
(2)求
关于
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b55ed6e3fdddb80a225f9c1a5f6d977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12f7eea27725016f0973e97d908c4d9.png)
(1)试求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562262bf2c7bcce52e9226796ddb1265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
名校
【推荐1】对于数列
,如果存在一个正整数
,使得对任意的
都有
成立,那么就把这样一类数列
称作周期为
的周期数列,
的最小值称作数列
的最小正周期,以下简称周期.例如当
时
是周期为1的周期数列,当
时
是周期为4的周期数列.
(1)设数列
满足
不同时为0
,求证:数列
是周期为6的周期数列,并求数列
的前2013项的和
;
(2)设数列
的前
项和为
,且
.
①若
,试判断数列
是否为周期数列,并说明理由;
②若
,试判断数列
是否为周期数列,并说明理由;
(3)设数列
满足
,数列
的前
项和为
,试问是否存在
,使对任意的
都有
成立,若存在,求出
的取值范围;不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef65559a6b44930addc23adeb8d854c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126141b8d68abc6a0823fade2f1b8127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082e8fd18cc10f578020188f254a2455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c002bdb39554b14fb5493781924069a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15987d51b64254b36a00be900799d166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a67afce3eba3ca099670e3ded418d9.png)
(2)设数列
![](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/5c07ba166ca9af1ffde9dd49876b17a4.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38ac38efc5f58e833f21c725e9711c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29a7d539f5f39eecf615febf9862109.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042896d1702c2c0345f21b63d35d766a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
名校
【推荐2】数列
的前
项和为
,且
是
和
的等差中项,等差数列
满足
,
.
(1)求数列
、
的通项公式;
(2)设
,数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aaee408bdec05bbdfcd4b841a331e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee04181b1fe91eb6a9abffc0ca2afe9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175005738672c8c1f431aac6333ab94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c522c1c881528ab6f9708f6bdd4c4db5.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/73e06b0fda8954c395f1a3ccfbc88698.png)
您最近一年使用:0次