1 . 已知数列
中,
,
.正项等比数列
的公比
,且满足
,
.
(1)证明数列
为等差数列,并求数列
和
的通项公式;
(2)如果
,求
的前n项和为
;
(3)若存在
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ac9d17bc8f166fc3894bf865ad6a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21cfd1ad0f4254be1d88c6577b6bbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90d19bcd582ed71cde0f18027174459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e3824ddd2210bd1e6313ad11dc8b13.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102abb18c888eb23d40708b97de140ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c39de50ed2f805d9c28aa7aadc46fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066141ba294715e4e725d59acfb85caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2 . 定义函数
,其中
表示不小于
的最小整数,如
,
.当
,
时,函数
的值域为
,记集合
中元素的个数为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab342d472fe409e73bee1be8a61774d3.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4e56d2f2ee3b7afaa8388bb0fdd806e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3788a125c33eee076151e215a9b02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0411aac4f1f068dc84271315c2e219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70e059359c17ba0f8211a9ed9a28fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3451933e11e7110ff28b4c14c1f8c304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361386446d504a14471b9fd89130f1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab342d472fe409e73bee1be8a61774d3.png)
您最近一年使用:0次
3 .
的整数部分是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f61f4f195149d7ff7eb304649c67a8.png)
您最近一年使用:0次
名校
4 . 已知等差数列
中,公差
,
,且
,
,
成等比数列.
求数列
的通项公式;
若
为数列
的前
项和,且存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd71318ddbb81a2d7ed7847e1ff744a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030ee00786b42b7f5eb8490c3b223dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb5ca241bb7c313ef0366d3ddba93bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feaf542829b99205948fa97442c3db92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061aa107ea2023b37be763a5c8b2f4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb26cd1601fe7e76e1e2dc0b4909324a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95149133cbe5ec386a29f9bf6ad1192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728c1c7345ccca5620c26591874c301c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211014b92b4ef16c9b85de1f885f8c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2016-12-03更新
|
4644次组卷
|
26卷引用:2017届河南豫北名校联盟高三理上精英对抗赛数学试卷1
2017届河南豫北名校联盟高三理上精英对抗赛数学试卷12017届河南豫北名校联盟高三文上精英对抗赛数学试卷12015届湖北省武汉华中师大附中高三5月考试文科数学试卷2016届黑龙江哈尔滨六中高三上期中理科数学试卷2017届河南南阳一中高三文上学期月考四数学试卷2016-2017学年广东省揭阳市第一中学高二上学期期末考试数学(文)试卷四川省绵阳市南山中学2018届高三二诊热身考试数学(理)试题广西贺州市2017-2018学年高二年级上学期期末质量检测数学(文)试题(已下线)《2018届优生-百日闯关系列》数学专题三 第五关 以数列与不等式相结合的综合问题为解答题河北省衡水中学2018届高三第十次模拟考试数学(理)试题安徽省郎溪中学2018-2019学高一下学期期末考试数学试题甘肃省武威第六中学2019-2020学年高三上学期第五次过关考试数学(理)试题2019届湖南长沙市第一中学高三月考试卷(二)数学理科试题四川省绵阳南山中学实验学校2019-2020学年高一下学期开学考试数学(理)试题(已下线)专题07 数列与不等式相结合问题(第二篇)-备战2020年高考数学大题精做之解答题题型全覆盖四川省棠湖中学2019-2020学年高一下学期第四学月考试数学(理)试题四川省棠湖中学2019-2020学年高一下学期第四学月考试数学(文)试题四川省成都市石室佳兴外国语学校2019-2020学年高一下学期期中数学试题广东省汕头市金山中学2021届高三下学期三模数学试题四川省广安市武胜县武胜烈面中学校2020-2021学年高一下学期期中数学试题安徽省六安市舒城中学2020-2021学年高二下学期第三次月考理科数学试题四川省绵阳南山中学实验学校2019-2020学年高一下学期开学考试数学(文)试题山西省孝义市实验中学2017-2018学年高二上学期第一次月考数学试题湖南省长沙市明德中学2022-2023学年高三上学期入学考试数学试题吉林省辽源市田家炳高级中学友好学校第七十二届2021-2022学年高三上学期期末考试数学(理)试题吉林省辽源市田家炳高级中学友好学校第七十二届2021-2022学年高三上学期期末考试数学(文)试题
14-15高三上·江西南昌·阶段练习
解题方法
5 . 已知函数
.
(1)求
的单调区间;
(2)已知数列
的通项公式为
,求证:
(
为自然对数的底数);
(3)若
,且
对任意
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce55fb50e4d80db3c2c7334a486087e1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10459464776a81e080722a72eaed0076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2151e0d3dfcf42c6aaa83d28919f41e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8105dc4ed50b8991078451a774e65d56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2016-12-03更新
|
406次组卷
|
3卷引用:第十一届高二试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)