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)
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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)
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2022-11-28更新
|
574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)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(已下线)专题15 数列求和-2
名校
解题方法
4 . 从条件①
;②
;③
中任选一个,补充在下面问题中,并给出解答.
已知数列
的前
项和为
,
,_____________.
(1)求
的通项公式;
(2)
表示不超过
的最大整数,记
,求
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3dbe8b2e565053935ace08a88ca0bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9288ce6e011292accb2e6a79422f0c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c34bc29e03e799169a595556349d78a.png)
已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853eace02560e7f1490694276c29a856.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6967087c7ceac60c4801fd6c6f86d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195431ccf2756a0db26f14b7b91a32a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f028f53bc97d6db2877c54ba3d69b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf875d39eb5d5f561228a38b9bc8b811.png)
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2022-10-10更新
|
1266次组卷
|
4卷引用:河北省保定市唐县第二中学2022-2023学年高二实验部下学期3月月考数学试题
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
|
938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)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
6 . 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
解题方法
7 .
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
8 . 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
名校
9 . 已知数列
中,
,
.
(1)求证:数列
是等比数列;
(2)求数列
的前
项和
,并求满足
的所有正整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4716ec121ba18b4511210c1a549f9cc6.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c3083c9192f3a3e1476d9f555eb923.png)
(2)求数列
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49763402b2f2023f0ba64c37924267d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2018-05-24更新
|
1753次组卷
|
10卷引用:【全国百强校】河北省衡水中学2017-2018学年高一下学期期末模拟数学试题
【全国百强校】河北省衡水中学2017-2018学年高一下学期期末模拟数学试题2015届山东省日照市高三3月模拟考试理科数学试卷2015届湖南长沙长郡中学等十三校高三第二次联考理科数学试卷2015届广东省汕头市潮南区高三高考模拟二理科数学试卷2015届浙江省杭州二中高三仿真考理科数学试卷2015-2016学年黑龙江省鹤岗一中高一下期中理科数学试卷黑龙江省穆棱市第一中学2016-2017学年高一下学期期中考试数学试题【全国百强校】天津市第一中学2018届高三下学期第五次月考数学(理)试题天津市南开中学2019-2020学年高三上学期12月月考数学试题2019届浙江省慈溪中学高三下学期高考适应性测试数学试题
10 . 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