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1 . 为引导游客领略传统数学研究的精彩并传播中国传统文化,某景点推出了“解数学题获取名胜古迹入场码”的活动.活动规则如下:如图所示,将杨辉三角第
行第
个数记为
,并从左腰上的各数出发,引一组平行的斜线,记第
条斜线上所有数字之和为
,入场码由两段数字组成,前段的数字是
的值,后段的数字是
的值,则( )
![](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/f02505396367e6eac8be3e6dee5584f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba726262d8c09f4a6187a27e32533679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835bb645ff22a34c78cad52b0aebf8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd32bf41f5d928ef002fc213946065a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/ba09d462-b928-4b9c-a9b3-528f985dddcf.png?resizew=263)
A.![]() | B.![]() |
C.![]() | D.该景点入场码为![]() |
您最近一年使用:0次
2023-09-30更新
|
909次组卷
|
6卷引用:第六章 计数原理(知识归纳+题型突破)(4)
(已下线)第六章 计数原理(知识归纳+题型突破)(4)(已下线)第06讲 第六章 计数原理 章末题型大总结(4)(已下线)模块五 专题3 全真能力模拟3江西省名校2024届高三上学期9月联合测评数学试题重庆市江北区第十八中学2023-2024学年高三上学期11月检测(一)数学试题辽宁省六校协作体2024届高三上学期期中联考数学试题
2 . 我国南宋时期的数学家杨辉,在他1261年所著的《详解九章算法》一书中,用如图的三角形解释二项和的乘方规律.此图称为“杨辉三角”,也称为“贾宪三角”.在此图中,从第三行开始,首尾两数为
,其他各数均为它肩上两数之和.
![](https://img.xkw.com/dksih/QBM/2021/7/20/2768335173107712/2793988819877888/STEM/a4a2071e-d54b-4260-9d37-1942fb2a7a43.png?resizew=246)
(1)把“杨辉三角”中第三斜列各数取出按原来的顺序排列得一数列:
,
,
,
,
,…,写出
与
的递推关系,并求出数列
的通项公式;
(2)已知数列
满足
,设数列
满足:
,数列
的前
项和为
,若
恒成立,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/2021/7/20/2768335173107712/2793988819877888/STEM/a4a2071e-d54b-4260-9d37-1942fb2a7a43.png?resizew=246)
(1)把“杨辉三角”中第三斜列各数取出按原来的顺序排列得一数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2278c80ff61dc116fa918c177ee4704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/facb460ed1932a6416738667afe85230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7759e794fb2ade6979c22342c72d7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b250e4276bf3f328b03a66765541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bfb610cc10e7d25ef05df4bf706a48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2021-08-25更新
|
1599次组卷
|
7卷引用:2023版 苏教版(2019) 选修第一册 突围者 第4章 第二节 课时3 等差数列的前n项和(2)
2023版 苏教版(2019) 选修第一册 突围者 第4章 第二节 课时3 等差数列的前n项和(2)江苏省常州市前黄高级中学2021届高三下学期5月高考适应性考试(一)数学试题山东省日照市2021-2022学年高三上学期开学校际联合考试数学试题山东省2022届高三上学期10月联合质量测评数学试题江西省宜春市丰城中学2023届高三(7-22班)上学期第二次段考数学(理)试题(已下线)专题11 数列前n项和的求法 微点4 裂项相消法求和(二)(已下线)模块四 专题7 新情境专练(基础)
解题方法
3 . 200多年前,10岁的高斯充分利用数字1,2,3,
,100的“对称”特征,给出了计算
的快捷方法.教材示范了根据高斯算法的启示推导等差数列的前
项和公式的过程.事实上,高斯算法的依据是:若函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
的图象关于点
对称,则
对
恒成立.已知函数
.
(1)求
的值;
(2)设
,
,记数列
的前
项和为
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c5cd89177a3934552efa0d7180e7cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b377a08ec48ad89158c9779b086f2f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5b41f8b5d0d7f18c2a6b746f6fe027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2d540cce5905a75539b4f4c2d64944.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ca6b43515d16806f9840ad2e2814ec.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae7320c43f9b89650706f230a5cbd9b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af430fc18567ecc9bc0faae9df6c4217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac8d00c56ac253f398526c9b3da6f04.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/a9fb028fe090cf1615fbee95042ab699.png)
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