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)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd810b777ea7c810453b560c078fe26.png)
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![](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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4卷引用:重庆市北碚区缙云教育联盟2024届高考零诊数学试题
重庆市北碚区缙云教育联盟2024届高考零诊数学试题广东省2024届高三上学期11月统一调研测试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)
名校
2 . 单位向量
,
,
的两两夹角为
,若实数
,
,
满足
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccfda9afde4441cfd1d4df5fe9622d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145ec8e9ef187afb4bf6d27a8ab8be22.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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3卷引用:重庆市北碚区西南大学附属中学校2024届高三上学期11月期中数学试题
名校
解题方法
3 . 已知数列
和
,
且
,函数
,其中
.
(1)求函数
的单调区间;
(2)若数列
各项均为正整数,且对任意的
都有
.求证:
(ⅰ)
;
(ⅱ)
,其中
为自然对数的底数.
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee03c109e4f64f3539de74ef30f06fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc65a38fceb3231eada88b96f0c63d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b0b716fda9b1efd9e47e2d80543f2d.png)
(ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf779c918958c14824cd7d952a4bb4bc.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462a81927ad910cd66ae9a5fd5813502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
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3卷引用:重庆西南大学附属中学校2023届高三上学期第三次月考数学试题
4 . 已知点
,点
是双曲线
:
左支上的动点,
为其右焦点,
是圆
:
上的动点,直线
交双曲线右支于
(
为坐标原点),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5757551de5911dd9d207abeffbbf392d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.过点![]() ![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.过![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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|
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2卷引用:重庆市西南大学附属中学校2021-2022学年高二下学期第三次月考数学试题
名校
解题方法
5 . 已知点A为圆台
下底面圆
上的一点,S为上底面圆
上一点,且
,
,
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31af799fd63896b640e833d617393480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e1f1a8f8efc198f933a0fe28f487f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf61b2c905d1eefe4198d43e8803cef.png)
A.直线SA与直线![]() ![]() |
B.直线SA与直线![]() ![]() |
C.圆台存在内切球,且半径为![]() |
D.直线![]() ![]() ![]() |
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名校
解题方法
6 . 已知函数
,且
.
(1)证明:当
时,
;
(2)设
且
,试比较
与
的大小,并给出证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7465633ebc62e5dece459298a1fda9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d1637fb61b268aed74d8c8ab8d5215.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3018f891b20bde560482522a476937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b68947b00b0cbdfe57ceda72ed09e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d686b2d3ed970131caa0f516ca8de6b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93beb75dc10a7590bd346756be2730e0.png)
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