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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解题方法
2 . 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)
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2023-02-07更新
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4卷引用:上海市市北中学2022届高三上学期期中数学试题
名校
解题方法
3 . 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)
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2022-03-31更新
|
1120次组卷
|
8卷引用:江苏省盐城市2022-2023学年高三上学期期中复习数学试题
江苏省盐城市2022-2023学年高三上学期期中复习数学试题北京市房山区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)(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)北京市北师大附属实验中学2021-2022高二下学期数学月考试题
名校
解题方法
4 . 科学数据证明,当前严重威胁人类生存与发展的气候变化主要是工业革命以来人类活动造成的二氧化碳排放所致.应对气候变化的关键在于“控碳”,其必由之路是先实现碳达峰,而后实现碳中和.2020年第七十五届联合国大会上,我国向世界郑重承诺力争在2030年前实现碳达峰,努力争取在2060年前实现碳中和.2021年全国两会的政府工作报告明确提出要扎实做好碳达峰和碳中和的各项工作,某地为响应国家号召,大力发展清洁电能,根据规划,2021年度火电发电量为8亿千瓦时,以后每年比上一年减少20%,2021年度清洁电能发电量为4亿千瓦时,以后每年比上一年增长25%.
(1)设从2021年开始的
年内火电发电总量为
亿千瓦时,清洁电能总发电量为
亿千瓦时,求
,
(约定
时为2021年);
(2)从哪一年开始,清洁电能总发电量将会超过火电发电总量?
(1)设从2021年开始的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098afe75dd67aa4c2d1f0b6616c4c1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
(2)从哪一年开始,清洁电能总发电量将会超过火电发电总量?
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