1 . 设
为整数.有穷数列
的各项均为正整数,其项数为m(
).若
满足如下两个性质,则称
为
数列:①
,且
;②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4daddea99be0888d1d6c560987c4bc2.png)
(1)若
为
数列,且
,求m;
(2)若
为
数列,求
的所有可能值;
(3)若对任意的
数列
,均有
,求d的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280f1e7d3e287061e928c064f2197e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7577a0af23649b4a2a25326fb9499c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b02eaacb42cc64295856fefdd5d287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4daddea99be0888d1d6c560987c4bc2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c39770fd747beb3f0431bd6e86876e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43703b905a9846c8f49f23b07ca661d.png)
您最近一年使用:0次
2023-05-05更新
|
1845次组卷
|
6卷引用:江苏省南京市南京外国语学校2024届高三下学期2月开学期初考试数学试题
江苏省南京市南京外国语学校2024届高三下学期2月开学期初考试数学试题北京市海淀区2023届高三二模数学试题北京卷专题18数列(解答题)(已下线)专题15 数列不等式的证明 微点1 反证法证明数列不等式北京市朝阳区2024届高三上学期数学期中模拟数学试题(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
解题方法
2 . 已知数列
中
,其前
项和记为
,且满足
.
(1)求数列
的通项公式;
(2)设无穷数列
,
,…
,…对任意自然数
和
,不等式
均成立,证明:数列
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.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/f085575b5c456ae641143d2d430458b0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7121ac4377ec9bcd071cb259678ab071.png)
(2)设无穷数列
![](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/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402b8223a5be456f2acb45f65648eb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
您最近一年使用:0次
2023-03-16更新
|
642次组卷
|
3卷引用:江苏省南京市中华、东外、镇江三校2022-2023学年高三下学期3月联考数学试题
江苏省南京市中华、东外、镇江三校2022-2023学年高三下学期3月联考数学试题广东省韶关市武江区广东北江实验学校2022-2023学年高二下学期第一次(3月)月考数学试题(已下线)第4章 数列 单元综合检测(重点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
3 . 若无穷数列
和无穷数列
满足:存在正常数A,使得对任意的
,均有
,则称数列
与
具有关系
.
(1)设无穷数列
和
均是等差数列,且
,
,问:数列
与
是否具有关系
?说明理由;
(2)设无穷数列
是首项为1,公比为
的等比数列,
,
,证明:数列
与
具有关系
,并求A的最小值;
(3)设无穷数列
是首项为1,公差为
的等差数列,无穷数列
是首项为2,公比为
的等比数列,试求数列
与
具有关系
的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd9630eef5312838c202cf054e9ee7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
(1)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e67d6abc5e1ab4c45046d1ee37e328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
(2)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2525f733e43b3a4558b83f10f20425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
(3)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d928d897331d22ce7a2d230ed7138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e116f14c30b56ba916164b2da784b4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
您最近一年使用:0次
2020-08-04更新
|
715次组卷
|
4卷引用:江苏省南京师范大附中2020届高三下学期6月高考模拟(1)数学试题
江苏省南京师范大附中2020届高三下学期6月高考模拟(1)数学试题上海市青浦区2021届高三上学期一模(期终学业质量调研)数学试题上海市青浦区2021届高三上学期一模数学试题(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
4 . 已知数列
的前
项和为
,把满足条件
的所有数列
构成的集合记为
.
(1)若数列
通项为
,求证:
;
(2)若数列
是等差数列,且
,求
的取值范围;
(3)若数列
的各项均为正数,且
,数列
中是否存在无穷多项依次成等差数列,若存在,给出一个数列
的通项;若不存在,说明理由.
![](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/0685ae037fd0aa7e3880d4e6eb811ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78a26e3eeac053424c52ab90f6a3490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1a641ee8906e6b3b1c2103be75c418.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6a0be735ff99ec17214e79fab3b8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5f42cec86c666af6a37956335c79b3.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1a641ee8906e6b3b1c2103be75c418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/723971083154cae2be17fbfbf8e931fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
您最近一年使用:0次