1 . 17到19世纪间,数学家们研究了用连分式求解代数方程的根,并得到连分式的一个重要功能:用其逼近实数求近似值.例如,把方程
改写成
①,将
再代入等式右边得到
,继续利用①式将
再代入等式右边得到
……反复进行,取
时,由此得到数列
,
,
,
,
,记作
,则当
足够大时,
逼近实数
.数列
的前2024项中,满足
的
的个数为(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cdd6f27334444c1884876b9e4cfe6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4174abb8a26d35b8df3bd4f30f431760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f302219f23caefd077370c29e557cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a74d79db6d58b2bfdb021d891cd822.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c07829bdcf009a84715f32c6784542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5237ae4a60796b4257e52a2c487c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63152e764f4f11e43d2895e07ea11bb.png)
A.1007 | B.1009 | C.2014 | D.2018 |
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2023-12-02更新
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4卷引用:广东省2024届高三上学期11月统一调研测试数学试题
广东省2024届高三上学期11月统一调研测试数学试题重庆市北碚区缙云教育联盟2024届高考零诊数学试题江苏省南京市南京师大附中2024届高三寒假模拟测试数学试题(已下线)专题04 数列及求和(分层练)(四大题型+14道精选真题)
解题方法
2 . 已知数列
满足
,
,且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6194b7839446c93adc1b49aefb9d7214.png)
A.![]() ![]() |
B.![]() |
C.![]() |
D.![]() ![]() ![]() |
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名校
解题方法
3 . 已知数列
满足
,且
,若使不等式
成立的
有且只有三项,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c492ef0c41f7a2f4c15fb27df44a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64174dea987ddd73fa4b73830e68a9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5bb5c64be2d5df6041b3acc26b9987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-11-27更新
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675次组卷
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2卷引用:四川省2024届高三上学期第三次联考(月考)理科数学试题
解题方法
4 . 数列
前n项和为
,且满足:
,
,
,
,下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06cbc030598d483c147065bf76b446bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/806e782cd67b94d31f073b277493742a.png)
A.![]() |
B.数列![]() |
C.![]() ![]() |
D.![]() ![]() |
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解题方法
5 . 已知无穷数列
的各项均为整数.设数列
的前
项和为
,记
中奇数的个数为
.
(1)若
,试写出数列
的前5项;
(2)证明:“
为奇数,且
为偶数”是“数列
为严格增数列”的充分非必要条件;
(3)若
(
为正整数),求数列
的通项公式.
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41274819307283f0a931fb244401733e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a229173b0f235a4da8aeb6d35f1325f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549d08f011d91ff3f40426a1db0adf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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6 . 若数列
满足
,则称数列
为
数列.记
.
(1)写出一个满足
,且
的
数列;
(2)若
,证明:
数列
是递增数列的充要条件是
;
(3)对任意给定的整数
,是否存在首项为1的
数列
,使得
?如果存在,写出一个满足条件的
数列
;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/3ff94d8db8d3d3d48949461cdeaebabd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9158db048850992ae4cace688253bf4c.png)
(1)写出一个满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ae3d3a898152e1e20488d3c224288d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3931e6266decbab4ab76b280f61bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c53bb14ff8d8c03c780fa46c06393d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f73eec2bbbfa166f874c39d05accb6.png)
(3)对任意给定的整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d72bba8881efc02361163a97c6dde32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2023-05-07更新
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1465次组卷
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5卷引用:北京市昌平区2023届高三二模数学试题
解题方法
7 . 已知
为非常数数列且
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a62ab68e3f500af2cc509bd733c0b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1292b689ae033d201118a390676a9747.png)
A.对任意的![]() ![]() |
B.对任意的正数![]() ![]() ![]() ![]() |
C.不存在![]() ![]() ![]() |
D.不存在![]() ![]() |
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8 . 数列
满足
,
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() |
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9 . 数列
满足
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ba3f90c7c48ad9d0316b7cea3e2b7c.png)
A.若![]() ![]() ![]() |
B.若存在无数个自然数![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() |
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2022-09-24更新
|
2040次组卷
|
6卷引用:湖北省荆门市龙泉中学2023届高三5月模拟数学试题
名校
解题方法
10 . 数列
满足
,
,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c0b5919a656fc74fdf0380f1573c1b.png)
A.若![]() ![]() ![]() |
B.若存在无数个自然数![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() |
您最近一年使用:0次
2022-09-23更新
|
1973次组卷
|
6卷引用:第4章 数列(基础、典型、易错、压轴)-【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)
(已下线)第4章 数列(基础、典型、易错、压轴)-【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)(已下线)模块三 专题3 小题满分挑战练(3) 期末终极研习室(高二人教A版)THUSSAT中学生标准学术能力2022-2023年度高三诊断性测试9月测试数学(理科)试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高二上学期9月阶段数学试题(已下线)专题17 数列(练习)-2湖北省襄阳市第五中学2022-2023学年高三上学期12月月考数学试题