1 . 如图,点
均在
轴的正半轴上,
,
,…,
分别是以
为边长的等边三角形,且顶点
均在函数
的图象上.
个等边三角形的边长
;
(2)设数列
的前
项和为
,求
.
(3)已知数列
的通项
,数列
中,
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce1e808127c5672eb1b47024e54c9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb99c20237aca8ff2ba640c28fbc5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a619e2751f422ae187505e95339d02fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b80801bd92f36541707eea1229685e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699bdb06cc1a8e431fd96fdd06f6d2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6e162176d244084d154bc50b598eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d876a9e0ab9abc3880410cfde910eb6.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/c6ef48976a52cc4a2be7c46a98426c0a.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c99ff3f6386113dbaa7b1e49612da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e1ee88beaddafb0d0a185c3a8e0dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a655f0f5afe3673c421af8a677b5154c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8427946085d576e0696e06cf4463c30f.png)
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2 . 我们知道,在平面内取定单位正交基底建立坐标系后,任意一个平面向量,都可以用二元有序实数对
表示.平面向量又称为二维向量.一般地,n元有序实数组
称为n维向量,它是二维向量的推广.类似二维向量,对于n维向量,也可定义两个向量的数量积、向量的长度(模)等:设
,
,则
;
.已知向量
满足
,向量
满足
.
(1)求
的值;
(2)若
,其中
,当
且
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c2af42141367e6e9ff0296c31daa7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b3b354facacd72bc68da6ac07be453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48d974578eb15ca117e0cb1b59788d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99aa60676891adca75eac086182a15c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581496116ddfba6dd03722fd771d5a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5babafd9f4e5c3c222ba25a3de66794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48d974578eb15ca117e0cb1b59788d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cb2f5c0569962cd7c1026f388cb661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99aa60676891adca75eac086182a15c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4492fb816272cd60cf3456c6a064020e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa3e5481ce1f11ea4cb1d1ddc71413.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301fa5679316c282923735aff9285559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95ac252e9126ab540c0102b941f0ee42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74cac554f22f3655ef6691b2ef821eac.png)
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解题方法
3 . 已知数列
共有
项,
,且
,记这样的数列
共有
个,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d99e8ff072b8df36d660427babf073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c2b428dfb6ff184554cbe2f299c23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba28a7346cf50329bede9d30d3bdaa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d99e8ff072b8df36d660427babf073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-03-21更新
|
429次组卷
|
3卷引用:山东省淄博市桓台县渔洋中学2023-2024学年高二下学期6月阶段性检测数学试题
名校
解题方法
4 . 若
,都存在唯一的实数
,使得
,则称函数
存在“源数列”
.已知
.
(1)证明:
存在源数列;
(2)(ⅰ)若
恒成立,求
的取值范围;
(ⅱ)记
的源数列为
,证明:
前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72620c113a6fe83273803a9ac24baa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a038de5f1ce88d3baa95c2fd30abf7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9e8b81696639769354c282560245f0b.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d5aa1a74419f1557aae998dbdadf87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(ⅱ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773bccec5a6fe68146daa59088db27d8.png)
您最近一年使用:0次
2024-03-12更新
|
2200次组卷
|
5卷引用:山东省泰安市第一中学2023-2024学年高二下学期3月月考数学试题
山东省泰安市第一中学2023-2024学年高二下学期3月月考数学试题福建省厦门市2024届高三下学期第二次质量检测数学试题(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题16-19辽宁省沈阳市第二中学2023-2024学年下学期期中考试数学试卷 江苏省南通市2024届高三高考考前押题卷(最后一卷)数学试题
5 . 已知数列
满足
,
,数列
的前
项和为
,设
,
表示不大于
的最大整数.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e3a9ec8c6f33cbecfe32a6323ef4f5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f4e1236d7dc0366d9523d0cbb426be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09961b42559a89a688c446183889fb1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.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/24a57996290794e082b21d8f1dfc322a.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/58e3a9ec8c6f33cbecfe32a6323ef4f5.png)
您最近一年使用:0次
6 . 已知数列
的前
项和为
,且满足
,则下列结论正确的是( )
![](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/851afb5fa82c3e4448ac7b674d143cdf.png)
A.![]() | B.![]() |
C.![]() | D.数列![]() ![]() |
您最近一年使用:0次
2023-10-07更新
|
1332次组卷
|
6卷引用:山东省日照市莒县第四中学2024届高三上学期第二阶段性考试数学试题
山东省日照市莒县第四中学2024届高三上学期第二阶段性考试数学试题山西省2024届高三上学期10月月考数学试题山西省金科大联考2024届高三上学期10月质量检测数学试题甘肃省酒泉市2023-2024学年高三上学期10月联考数学试题(已下线)模块六 专题6 全真拔高模拟2(已下线)考点9 数列通项公式 2024届高考数学考点总动员【练】
解题方法
7 . 记
为数列
的前
项和,已知
,
.
(1)求
的通项公式;
(2)令
,证明:
.
![](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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6b7eeda1ca25d1630e3eca48061c7d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053d545d85e8e4b7f96e41500efd6945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3593087fb880597ad563d015c7027ca.png)
您最近一年使用:0次
名校
解题方法
8 . 已知首项不为0的等差数列
,公差
(
为给定常数),
为数列
前
项和,且
为
所有可能取值由小到大组成的数列.
(1)求
;
(2)设
为数列
的前
项和,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacf726c1efc076e9c33d668159bec84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/89dea3b1e936a165716a055ad31b555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f011e3d1d8961056cd7c334bd36edf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ffd4e5eab74838bcaa63202bdb9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b93c0a7a990bfd7c5b0af6cbc0f02b.png)
您最近一年使用:0次
2023-02-22更新
|
4397次组卷
|
13卷引用:山东省淄博市第一中学2022-2023学年高二下学期第一次学习质量检测数学试题
山东省淄博市第一中学2022-2023学年高二下学期第一次学习质量检测数学试题山东省青岛市青岛第五十八中学2023-2024学年高三上学期10月月考数学试题山东省菏泽市2023届高三下学期一模联考数学试题山东省烟台市芝罘区高中协同联考2023届高三三模数学试题(已下线)专题4 数列专题13数列(解答题)(已下线)专题15 数列求和-1(已下线)专题15 数列不等式的证明 微点6 数列不等式的证明综合训练(已下线)第四节 数列求和 (讲)(已下线)专题05 等比数列与数列综合求和-2023-2024学年高二数学期末复习重难培优与单元检测(人教A版2019)(已下线)数列与不等式专题04数列求和(裂项求和)(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
9 . 已知数列
满足
,
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b293ef8b6f41032dd6016ce4defd9eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
A.数列![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-02-13更新
|
837次组卷
|
3卷引用:山东省德州市第一中学2023-2024学年高二下学期3月月考数学试题
山东省德州市第一中学2023-2024学年高二下学期3月月考数学试题重庆市南开中学校2022-2023学年高二下学期开学考试数学试题(已下线)微考点4-2 新高考新试卷结构数列的通项公式的9种题型总结
解题方法
10 . 已知等差数列
为递增数列,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef3d37853abde3139a81bc5421762b9.png)
(1)求
的通项公式;
(2)若数列
满足
,求
的前
项和的最大值、最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/123b6afa3d8be7389913ec3cfe521510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef3d37853abde3139a81bc5421762b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733969643c55ec0ddfddd781a6545778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a304ee61802c1cc89b60063332b52bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733969643c55ec0ddfddd781a6545778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
您最近一年使用:0次