解题方法
1 . 数列
中,给定正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
,
.定义:数列
满足
,称数列
的前
项单调不增.
(Ⅰ)若数列
通项公式为:
,求
;
(Ⅱ)若数列
满足:
,求证
的充分必要条件是数列
的前
项单调不增;
(Ⅲ)给定正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
,若数列
满足:
,且数列
的前
项和为
,求
的最大值与最小值.(写出答案即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad58ed5a48295f7f18a5225ba8d587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9560ef128e41e22e920cad05478703a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a1a71b07e029a192496616fb7b51ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8b1004db0d954d20c6254a7308847f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675123cce20a9ce670fb7ae18943bde7.png)
(Ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f28ba33c7d7fe2730f4ac058ac2f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a2be1c992655c9c3aa49804d2eb4d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅲ)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad58ed5a48295f7f18a5225ba8d587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198955f27e060b6628f703d0b4d278a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d7b4bb12628d5ed455d814b8aafa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8861a2221f16a11415179361c7058a.png)
您最近一年使用:0次
2 . 对于数列A:
,经过变换T:交换A中某相邻两段的位置(数列A中的一项或连续的几项称为一段),得到数列
.例如,数列A:
经交换M,N两段位置,变换为数列
:
.设
是有穷数列,令
.
(1)如果数列
为3,2,1,且
为1,2,3.写出数列
;(写出一个即可)
(2)如果数列
为9,8,7,6,5,4,3,2,1,
为5,4,9,8,7,6,3,2,1,
为5,6,3,4,9,8,7,2,1,
为1,2,3,4,5,6,7,8,9.写出数列
;(写出一组即可)
(3)如果数列
为等差数列:2015,2014,…,1,
为等差数列:1,2,…,2015,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bbf1fc7753df7951558e56b71b78c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a403f562ca2b40d07069aace053e8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a60554299801b8c94f80e04398e589.png)
(1)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
(2)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfefd19874aeff8340735b3df468333.png)
(3)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次
名校
3 . 已知无穷数列
满足
,其中
表示x,y中最大的数,
表示x,y中最小的数.
(1)当
,
时,写出
的所有可能值;
(2)若数列
中的项存在最大值,证明:0为数列
中的项;
(3)若
,是否存在正实数M,使得对任意的正整数n,都有
?如果存在,写出一个满足条件的M;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba6d5fdf4c491c1332483be3cfab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37f161c1dd788025cef9910858df7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c03a27be8ae82e24b86cc52a92204c28.png)
(1)当
![](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/daf464629fa321a6ff7401ab79f07083.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a65d8762e567f485f39f81564b593a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5612ce06759d0f77ca029d10083f7d1e.png)
您最近一年使用:0次
2023-05-05更新
|
3811次组卷
|
19卷引用:北京市朝阳区2023届高三二模数学试题
北京市朝阳区2023届高三二模数学试题北京卷专题18数列(解答题)北京一零一中学2024届高三上学期统考一数学试题北京市景山学校2024届高三上学期10月月考数学试题(已下线)北京市第四中学2024届高三上学期10月月考数学试题北京市东城区东直门中学2024届高三上学期期中数学试题北京市第二中学2023-2024学年高三下学期开学考试数学试卷北京市顺义区第九中学2023-2024学年高三下学期3月月考数学试题北京市海淀实验中学2024届高三上学期10月月考数学试题(已下线)北京市第四中学2024届高三上学期10月月考数学试题变式题16-21(已下线)专题01 条件开放型【练】【北京版】2024年全国普通高中九省联考仿真模拟数学试题(二)(已下线)高三数学开学摸底考02(新考法,新高考七省地区专用)(已下线)【一题多变】取大取小 分类讨论广东省2024届高三数学新改革适应性训练二(九省联考题型)(已下线)数列新定义(已下线)(新高考新结构)2024年高考数学模拟卷(二)上海市杨浦区复旦大学附属中学2024届高三下学期3月月考数学试题广东省云浮市云安区云安中学2024届高三下学期3月模拟考试数学试题
名校
4 . 将所有平面向量组成的集合记作
,
是从
到
的对应关系,记作
或
,其中
、
、
、
都是实数,定义对应关系
的模为:在
的条件下
的最大值记作
,若存在非零向量
,及实数
使得
,则称
为
的一个特殊值;
(1)若
,求
;
(2)如果
,计算
的特征值,并求相应的
;
(3)若
,要使
有唯一的特征值,实数
、
、
、
应满足什么条件?试找出一个对应关系
,同时满足以下两个条件:①有唯一的特征值
,②
,并验证
满足这两个条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5938410a3d39a1f3f4df67faf99ab5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39549972b3c02bd84637471fb171ae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6951a7aad8c0f5a06ad8bb6fb8f0f544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9c5e3816909bd49a229130af166698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e6644ad87b4054c76468bdf95baa8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393f7419709b2c20d4234b63fc4c9fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6938ce64829c28318021579c6e45b4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f17de8ca8bc0eeecd338e423f787e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e6644ad87b4054c76468bdf95baa8f.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df049cbc7425555ea643fbb824a0df63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552355ddba8eef1ca3bf15eb53d79622.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2322e48ae3b2a166f061eb4aaf39f355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](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/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da66c64d70ef7d57d645e11f2a1b1e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
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2020-02-13更新
|
640次组卷
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3卷引用:2020届北京市第22中学高三第一学期第二次阶段性考试数学试题