2013·上海浦东新·三模
名校
1 . 已知数列
,
满足:
.
(1)若
,求数列
的通项公式;
(2)若
,且
.
① 记
,求证:数列
为等差数列;
② 若数列
中任意一项的值均未在该数列中重复出现无数次,求首项
应满足的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3249883fe3dab15d47302fef4f37146b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3473964e962ac6304ee4a66a239f9e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93d57876a4346a2c065c1c2c69e6510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e19845d07c89edf3424ef3caf45810.png)
① 记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a79cf657c6b6d301bfd1e748bff12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
② 若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245588805f41199996befd1d3d5c7c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
2016-12-02更新
|
1339次组卷
|
7卷引用:2013届上海市浦东新区高三第三次模拟理科数学试卷
(已下线)2013届上海市浦东新区高三第三次模拟理科数学试卷2016届江苏省南京市高三第三次学情调研测试数学试卷江苏省东台市2017届高三5月模拟数学试题2017年上海市交大附中嘉定分校高三下学期三模数学试题2016届上海市上海交大附中嘉定分校高三5月(三模)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(已下线)专题10 数列通项公式的求法 微点10 数列通项公式的求法综合训练
真题
2 . 已知各项均为正数的两个数列
和
满足:
,
,
(1)设
,
,求证:数列
是等差数列;
(2)设
,
,且
是等比数列,求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://img.xkw.com/dksih/QBM/2012/6/27/1570901069398016/1570901075247104/STEM/956f280ec8d7449399a3c7e83d87b7bb.png)
![](https://img.xkw.com/dksih/QBM/2012/6/27/1570901069398016/1570901075247104/STEM/e8d84e8ff3274d8c91aa7f11bba18465.png)
(1)设
![](https://img.xkw.com/dksih/QBM/2012/6/27/1570901069398016/1570901075247104/STEM/14c6ecca62b84a7d85e2fc2eedeb5bb0.png)
![](https://img.xkw.com/dksih/QBM/2012/6/27/1570901069398016/1570901075247104/STEM/e8d84e8ff3274d8c91aa7f11bba18465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd7524e299180306a05a680e2298ccf.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2012/6/27/1570901069398016/1570901075247104/STEM/b6928c583fa547d1b4e2c735000c0f13.png)
![](https://img.xkw.com/dksih/QBM/2012/6/27/1570901069398016/1570901075247104/STEM/e8d84e8ff3274d8c91aa7f11bba18465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://img.xkw.com/dksih/QBM/2012/6/27/1570901069398016/1570901075247104/STEM/bcf0f87c09eb42bd8b47f0112f3d1a5e.png)
您最近一年使用:0次
2016-12-01更新
|
3594次组卷
|
3卷引用:2012年全国普通高等学校招生统一考试数学(江苏卷)
2012年全国普通高等学校招生统一考试数学(江苏卷)专题10.4 推理与证明(练)-江苏版《2020年高考一轮复习讲练测》(已下线)专题6.5 数列的综合问题(练)-江苏版《2020年高考一轮复习讲练测》
真题
3 . 对于项数为m的有穷数列数集
,记
(k=1,2,…,m),即
为
中的最大值,并称数列
是
的控制数列.如1,3,2,5,5的控制数列是1,3,3,5,5.
(1)若各项均为正整数的数列
的控制数列为2,3,4,5,5,写出所有的
;
(2)设
是
的控制数列,满足
(C为常数,k=1,2,…,m).
求证:
(k=1,2,…,m);
(3)设m=100,常数
.若
,
是
的控制数列,
求
.
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/2b0ff7d0a5534c47a187f63321aa63df.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/c9eb5ef62e064fc6bcaaeaa26ea738e6.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/513040b1110c4e2daef20ec1f1f63ca2.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/e87c0cf6094f41818bc77d67ebc144c6.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/6d972c3ad65a4a2991f16123a016974f.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/2b0ff7d0a5534c47a187f63321aa63df.png)
(1)若各项均为正整数的数列
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/2b0ff7d0a5534c47a187f63321aa63df.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/2b0ff7d0a5534c47a187f63321aa63df.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/6d972c3ad65a4a2991f16123a016974f.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/2b0ff7d0a5534c47a187f63321aa63df.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/f24f5e7fcbbd4a86a6d9f51dd5574723.png)
求证:
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/ac5b489281da4a33b5c33dcc232c58b9.png)
(3)设m=100,常数
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/43433998e87d495d8fa11eb84e197878.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/08af965a17a44eb6b854e2ef1415ea8f.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/6d972c3ad65a4a2991f16123a016974f.png)
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/2b0ff7d0a5534c47a187f63321aa63df.png)
求
![](https://img.xkw.com/dksih/QBM/2012/6/14/1570886267199488/1570886272892928/STEM/c6c501a37bc245e8904d034a77b7dcd9.png)
您最近一年使用:0次
12-13高三上·广东·期末
解题方法
4 . 已知数列
,
,其中
是方程
的两个根.
(1)证明:对任意正整数
,都有
;
(2)若数列
中的项都是正整数,试证明:任意相邻两项的最大公约数均为1;
(3)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b53f92137045409f92541ca8b622c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cdd6f27334444c1884876b9e4cfe6f.png)
(1)证明:对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316b5d6779890069e877f081d1833883.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff3cb714115d9604b804887c8dc4601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dec85a1d2c4070f93b8d201af8eebc5.png)
您最近一年使用:0次
12-13高三上·上海黄浦·期末
5 . 已知
,且
,数列
满足
.
(1) 求证数列
是等比数列;
(2)数列
的通项公式
;
(3)若
满足
,试用数学归纳法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034bc3e9924cff6b8403011d8cff8d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a44fd871e325084e136f9502483fa26.png)
(1) 求证数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99fb7eb3c3539236ad4b19e9ce71ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d57ab4dc62901dfb07e4f79819b94f.png)
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12-13高三上·北京西城·期末
6 . 已知数列
.如果数列
满足
,
,其中
,则称
为
的“衍生数列”.
(Ⅰ)若数列
的“衍生数列”是
,求
;
(Ⅱ)若
为偶数,且
的“衍生数列”是
,证明:
的“衍生数列”是
;
(Ⅲ)若
为奇数,且
的“衍生数列”是
,
的“衍生数列”是
,….依次将数列
,
,
,…的第
项取出,构成数列
.证明:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d620a71a9448d3a5be7fd8d5fea7094e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad083576ed8ff766b6d7c2a59a1c448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7e6327ecd86c682863f4a89e619fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da65bfc5919df189631c53048808e4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7304f4a3860fb2ce6535b51166d21446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(Ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232a4957e93a83aa5f3dd7215b9be594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5be81852e6ae92135ad336a919e601c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0016748ebec31c2f1bd490cb53994536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ab198a23f10c51c5796772e9147305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefcd32ac3e94ba73126ab1c29f0dda2.png)
您最近一年使用:0次
2016-12-01更新
|
1164次组卷
|
3卷引用:2012届北京市西城区高三上学期期末考试理科数学试卷
7 . 一青蛙从点
开始依次水平向右和竖直向上跳动,其落点坐标依次是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963001e3eb70f73ccca6e09dac87a8dc.png)
,(如图所示,
坐标以已知条件为准),
表示青蛙从点
到点
所经过的路程.
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572968060739584/1572968067170304/STEM/19f3c5671eea463d8812e02e4ebb993c.png)
(1)若点
为抛物线
(
)准线上一点,点
均在该抛物线上,并且直线
经过该抛物线的焦点,证明
.
(2)若点
要么落在
所表示的曲线上,要么落在
所表示的曲线上,并且
,试写出
(不需证明);
(3)若点
要么落在
所表示的曲线上,要么落在
所表示的曲线上,并且
,求
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c75612d583fe1c593fddf0df3b07d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963001e3eb70f73ccca6e09dac87a8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2916cb0fd1273b181640bf9b86f5496a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c75612d583fe1c593fddf0df3b07d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://img.xkw.com/dksih/QBM/2016/8/8/1572968060739584/1572968067170304/STEM/19f3c5671eea463d8812e02e4ebb993c.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c75612d583fe1c593fddf0df3b07d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0aa23696b63c7d2d2950980a2c8cdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfbb8b3c14e9617655321cab31acebc.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a66b3f63ad767a5cd4a92e7d9d198b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8845ac2aec1ed25f501e53b9b4e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f4ee7d7a59449ecfccfa8ebe6588e7.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a66b3f63ad767a5cd4a92e7d9d198b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3627436bfaf5a3e38938acc762352e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d55d2201d4d9aa7846b17a249ac528b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de7649e71f3893dffaa4c5d8d9c42d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2016-12-01更新
|
934次组卷
|
4卷引用:2012届上海市七宝中学高三模拟考试理科数学
(已下线)2012届上海市七宝中学高三模拟考试理科数学2016届上海市七宝中学高三模拟理科数学试卷2016届上海市七宝中学高三模拟考试数学(理)试卷2016届上海市闵行区七宝中学高三下学期适应性考试(三模)(理)数学试题
11-12高三·上海奉贤·期末
解题方法
8 . (理)对于数列
,如果存在最小的一个常数
,使得对任意的正整数恒有
成立,则称数列
是周期为
的周期数列.设
,数列前
项的和分别记为
,则
三者的关系式_____________________
(文)已知数列
的通项公式为
,那么满足
的正整数
=________
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/b75d70bcf01c4587bb33605541832a16.png?resizew=30)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/b35accbcb9ec44098bb9b48b2b34c40d.png?resizew=69)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/242c1e9b3af94fb4b441dfea03fb423b.png?resizew=64)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/b75d70bcf01c4587bb33605541832a16.png?resizew=30)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/b6c949e719a447c6b4025d9d5f129cad.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/fd112a7005f64d9383ee29ed3f59f033.png?resizew=180)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/f0e78e50590c4e74a83198192de3f310.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/8ba9867b78574fcd9d0af4ad65a8b8f5.png?resizew=66)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935681536/STEM/8ba9867b78574fcd9d0af4ad65a8b8f5.png?resizew=66)
(文)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e99bc30c7df18ec527142905327cb9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9534ed1c74894c735ffa3c71df721343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
11-12高三上·上海·期中
名校
9 . 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
的周期数列,当
时
是周期为
的周期数列.
(1)设数列
满足
,
,
(
、
不同时为
),且数列
是周期为
的周期数列,求常数
的值;
(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/8a97f6ce4374c1bd842d86d4b23c5130.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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a126883fcc5109ee41a021436c5ca826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0393abbce53f9f07a8f49890290e1f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55ef34345210312db273ab4981c40f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.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/63c76e1df87be17eae7f5517c7de6f0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.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/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b492f66b5611f650e1afbbde8c1abd6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
您最近一年使用:0次
10 . 已知数列
中,
(
是不等于
的常数),
为数列
的前
项和,若对任意的正整数
都有
.
(1)证明:数列
为等差数列;
(2)记
,求数列
的前
项和
;
(3)记
,是否存在正整数
,使得当
时,恒有
?若存在,证明你的结论,并给出一个具体的
值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fb25ac91603562339c3e698af1f610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df945ccc3744817dc13ead49253f5fe.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeeddd635af93a58c57aa1feb0843bd6.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)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5a17fd4b8cebf8187e824d9a7902c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79620f688a16fe02159520b99e6b0d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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