1 . 已知
为正整数,数列
,记
.对于数列
,总有
,则称数列
为
项
数列.若数列
,均为
项
数列,定义数列
,其中
.
(1)已知数列
,求
的值;
(2)若数列
均为
项
数列,求证:
;
(3)对于任意给定的正整数
,是否存在
项
数列
,使得
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752fd51a1f77da353ce6b1f60a541484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf2db1d7b80adf8e2f9e1166e38d129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a1e9876a6eb9cd53f9429c76582b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1ee6963151926f01ffd3397588b1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9685faad8329a30524372ce517ccafb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1ee6963151926f01ffd3397588b1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393a788648e88082e87770cd08a232d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffbbb6694b6e8c47f93cc16fdadf734.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac989f284ebccffe400dc33abc0c4bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfefa1b4b591f44ed19304e74003744.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1ee6963151926f01ffd3397588b1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68ff25db435cce5fe13c17c1b98395.png)
(3)对于任意给定的正整数
![](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/8c1ee6963151926f01ffd3397588b1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b12c2f01a02302617a35c87aade849e.png)
您最近一年使用:0次
2 . 已知首项为正数的等差数列
的公差为2,前
项和为
,满足
.
(1)求数列
的通项公式;
(2)令
,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/4cc6f5b50cb2b4c43479a07a936f81e4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf9615c9ebe63ef633c22818c41e452.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)
您最近一年使用:0次
2024-01-17更新
|
2854次组卷
|
7卷引用:专题06 数列
(已下线)专题06 数列重庆市主城区2024届高三上学期第一次学业质量检测数学试题江西省上饶艺术学校2024届高三上学期1月月考数学试题(已下线)第2讲:复杂数列通项和求和【练】湖北省武汉市马房山中学2024届高三上学期期末综合测评数学试题(已下线)题型18 4类数列综合(已下线)信息必刷卷02(江苏专用,2024新题型)
3 . 数列{an}满足:
,点
在函数
的图象上,其中k为常数,且
.
(1)若
,
,
成等比数列,求k的值;
(2)当
时,求数列
的前
项的和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7c9a6445ab0ddee8d69c9b3784cce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
您最近一年使用:0次
2022-11-28更新
|
575次组卷
|
9卷引用:河北省冀东名校2022-2023学年高三上学期期中调研考试数学试题
河北省冀东名校2022-2023学年高三上学期期中调研考试数学试题陕西省西安中学2021届高三第一次仿真考试数学(理)试题(已下线)热点08 利用“不动点”法巧解数列问题-2022年高考数学核心热点突破(全国通用版)【学科网名师堂】(已下线)考点25 数列求和-备战2022年高考数学(理)一轮复习考点帮(已下线)考点24 数列求和-备战2022年高考数学(文)一轮复习考点帮(已下线)专题7.5 数列的综合应用(练)- 2022年高考数学一轮复习讲练测(新教材新高考)(已下线)专题15 数列求和-2上海市奉贤区致远高级中学2022-2023学年高二上学期12月月考数学试题山东省青岛市青岛第五十八中学2022-2023学年高二上学期期末数学试题
4 . 已知数列
满足
,
,记数列
的前n项和为
.
(1)求
的值;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7bdaaf8b0adf10bf2ef6c1255b1dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d04b08ccdf5d4230ce37b505e3a81cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21041b03840e637469cd6658e6e07ca8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
名校
5 . 已知a1,a2,…,an是由n(n∈N*)个整数1,2,…,n按任意次序排列而成的数列,数列{bn}满足bn=n+1﹣ak(k=1,2,…,n).
(1)当n=3时,写出数列{an}和{bn},使得a2=3b2;
(2)证明:当n为正偶数时,不存在满足ak=bk(k=1,2,…,n)的数列{an};
(3)若c1,c2,…,cn是1,2,…,n按从大到小的顺序排列而成的数列,写出ck(k=1,2,…,n),并用含n的式子表示c1+2c2+…+ncn.
(参考:12+22+…+n2=
n(n+1)(2n+1))
(1)当n=3时,写出数列{an}和{bn},使得a2=3b2;
(2)证明:当n为正偶数时,不存在满足ak=bk(k=1,2,…,n)的数列{an};
(3)若c1,c2,…,cn是1,2,…,n按从大到小的顺序排列而成的数列,写出ck(k=1,2,…,n),并用含n的式子表示c1+2c2+…+ncn.
(参考:12+22+…+n2=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
您最近一年使用:0次
2022-06-14更新
|
941次组卷
|
5卷引用:信息必刷卷03
(已下线)信息必刷卷032016届上海市黄浦区高三上学期期末调研测试(文)数学试题(已下线)专题10 推理与证明-【备战高考】2021年高三数学高考复习刷题宝典(解答题专练)江苏省连云港市连云港高级中学2023-2024学年高三下学期4月阶段测试数学试题广东省乐昌市第一中学2021-2022学年高二下学期6月学科测试数学试题
名校
解题方法
6 .
为数列
的前
项和满足:
.
(1)设
,证明
是等比数列;
(2)求
.
![](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/f68c466e8bc7621b3523c49a30d1bd55.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e680f28daa101a42903ef44cf6e6894a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2020-05-23更新
|
629次组卷
|
4卷引用:河北省石家庄市第二中学2019-2020学年高三下学期教学质量检测(开学考试)数学(理)试题
名校
7 . 已知等差数列
的前
项的和为
,
.
(1)求数列
的通项公式;
(2)设
,求
;
(3)设
,
表示不超过
的最大整数,求
的前1000项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0e41849b91d8e7993b4540a32819ed.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f84250d0a6b7e44ac153bd2a8b83828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b223fcd2dc76b5926f88bb6c79eef99a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f010ba9cdd565ba7a3c236d722fae6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d983b63ac9f95cdd7522ccfa0df2b227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2e1becf98c5710b1a3d393034ed006.png)
您最近一年使用:0次
2019-03-28更新
|
1450次组卷
|
2卷引用:【全国百强校】河北省武邑中学2019届高三下学期第一次质检数学(理)试题
8 . 已知等差数列
的前
项和为
,且满足
.
(1)求数列
的通项公式;
(2)设
,求数列
的前
项和为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/10649c21860ab2e9551c97aa2d15b7aa.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba61538d54a340f5a01dcef01049b958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.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
名校
解题方法
9 . 已知
为等差数列
的前
项和,且
.记
,其中
表示不超过
的最大整数,如
.
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18a28c9fb6ef74419e9dd154cd9a185.png)
(2)求数列
的前200项和.
![](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/f0f453cb1438c6632bfded44015a6b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/511bf0fe9bd2b7016e88adba24828dc9.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/8c97b2fda777eb1a17b8173bb184387e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18a28c9fb6ef74419e9dd154cd9a185.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
您最近一年使用:0次
2018-04-24更新
|
658次组卷
|
3卷引用:【全国百强校】河北省衡水中学2018届高三下学期押题卷第四套数学(文)试题
名校
10 . 已知函数
,
.
(1)当
时,求函数
的图象在
处的切线方程;
(2)若函数
在定义域上为单调增函数.
①求
最大整数值;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624ae3a8ee55c7e72953741a07db23a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8833b3e4dfecca27ceb587b9ab0e0095.png)
您最近一年使用:0次
2018-01-18更新
|
1433次组卷
|
7卷引用:河北省衡水中学2018届高三上学期八模考试数学(理)试题