1 . 九章算术是我国古代内容极为丰富的数学名著,斑斓夺目的数学知识中函数尤为耀眼,加上数列知识的加持,犹如锦上添花.下面让我们通过下面这题来体会函数与数列之间的联系.已知
,
.
(1)求函数
的单调区间
(2)若数列
(
为自然底数),
,
,
,
,求使得不等式:
成立的正整数
的取值范围
(3)数列
满足
,
,
.证明:对任意的
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c24b58dc9e82b38b54be9e1e0cbf93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68072473a5106f93e3026d992859f7a1.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5e599c1b27a08b74ba20788d1891ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292b7800ba829f3f458cd6c23edf68a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f043bbedf5095c1d4478f94e491d0783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b1b7450d05f5d5ff2e9df74e3792e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06aaadbbbd40e7259ee76cbfeaebc25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176c580ac372c687eea2f4dc1eeb1f20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cb342c191aa0c8a897926a001497397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be0169dbd1fd354ca6cbc2673c7f543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05130dbf9769d55b5ce23fd251c047d1.png)
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2 . 对于数列
,
,其中
,对任意正整数
都有
,则称数列
为数列
的“接近数列”.已知
为数列
的“接近数列”,且
,
.
(1)若
(
是正整数),求
,
,
,
的值;
(2)若
(
是正整数),是否存在
(
是正整数),使得
,如果存在,请求出
的最小值,如果不存在,请说明理由;
(3)若
为无穷等差数列,公差为
,求证:数列
为等差数列的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78393519255d80cb3c118a0d71f15511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4719086a4e785f6b5fdb429a313ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20c7b6daa1896a8a274c53f78562987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26617babc02c5fcd7f26963a39d63bcd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce6549c5171680493c49b60b7556e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390a3ae2949dfbf5a342bda3372d3149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ba29be0a4f589c51de211609728ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf4973ccdd9289ee99369aaa916cb6c.png)
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2022-12-16更新
|
729次组卷
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4卷引用:上海市徐汇区2023届高三一模数学试题
上海市徐汇区2023届高三一模数学试题(已下线)专题16 数列新定义题的解法 微点2 数列新定义题的解法(二)上海市洋泾中学2023-2024学年高二上学期10月质量检测数学试题湖南省长沙市湖南师范大学附属中学2024届高三下学期高考模拟(三)数学试卷
名校
解题方法
3 . 对于数列
,若存在正数
,使得对任意
,
,都满足
,则称数列
符合“
条件”.
(1)试判断公差为2的等差数列
是否符合“
条件”?
(2)若首项为1,公比为
的正项等比数列
符合“
条件”.求
的范围;
(3)在(2)的条件下,记数列
的前
项和为
,证明:存在正数
,使得数列
符合“
条件”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04c7ba0ffd54e60b2829f4440c91ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e103afdf96430454d8409592a2c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca3fafacd6a4d9df495f3563d22c286.png)
(1)试判断公差为2的等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a390a0f7b1073ebeb024a225672a7e.png)
(2)若首项为1,公比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd07cd3600f1b5ab12e079890630edcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)在(2)的条件下,记数列
![](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/6ed1e9cdd5a82f29ec89b2c53b4fa6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cba3bb73f0c643c79b53db038c3706a.png)
您最近一年使用:0次
2023-02-07更新
|
689次组卷
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4卷引用:模块九 数列-2
名校
解题方法
4 . 若无穷数列{
}满足如下两个条件,则称{
}为无界数列:
①
(n=1,2,3......)
②对任意的正数
,都存在正整数N,使得n>N,都有
.
(1)若
,
(n=1,2,3......),判断数列{
},{
}是否是无界数列;
(2)若
,是否存在正整数k,使得对于一切
,都有
成立?若存在,求出k的范围;若不存在说明理由;
(3)若数列{
}是单调递增的无界数列,求证:存在正整数m,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
②对任意的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700458c01a7ad031e27d80ed43e9e882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a701eb81a1e88c69357f9eae5915ee.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff1c33b81ac2f065d37faef37504bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee912af5e2313d631ff3016ca7cc32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff1c33b81ac2f065d37faef37504bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fef5f2a4235817fb704d29e08766e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bec3181d9f88a68fb7470d0c9beb183.png)
(3)若数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7407503edea1b02e3084387c8a328d9e.png)
您最近一年使用:0次
2022-03-31更新
|
1120次组卷
|
8卷引用:北京市第五中学2022-2023学年高二下学期期中考试数学试题
北京市第五中学2022-2023学年高二下学期期中考试数学试题北京卷专题18数列(解答题)北京市房山区2022届高三一模数学试题(已下线)临考押题卷01-2022年高考数学临考押题卷(北京卷)北京市北师大附属实验中学2021-2022高二下学期数学月考试题(已下线)必刷卷03-2022年高考数学考前信息必刷卷(新高考地区专用)(已下线)重难点08 七种数列数学思想方法-2江苏省盐城市2022-2023学年高三上学期期中复习数学试题