1 . 已知数列
的前n项和为
,且满足
,
.
(1)判断
是否为等差数列?并证明你的结论;
(2)求
和
;
(3)求证:
.
![](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/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a022b4111eeada0a90412ab74e2ad325.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8050391385b496e9c059201e4f12600a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31066efaa85cde2cedf2cb065bbc162a.png)
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2024-01-11更新
|
1622次组卷
|
4卷引用:上海市青浦高级中学2023-2024学年高二上学期期末考试数学试题
上海市青浦高级中学2023-2024学年高二上学期期末考试数学试题(已下线)每日一题 第26题 由Sn求an 作差检验(高二)(已下线)模块六 大招4 数列不等式的放缩河南省南阳市第一中学校2023-2024学年高二下学期第一次月考数学试题
名校
解题方法
2 . 已知椭圆
过点
,且离心率为
.设
,
为椭圆
的左、右顶点,
为椭圆上异于
,
的一点,直线
,
分别与直线
相交于
,
两点,且直线
与椭圆
交于另一点
.
(1)求椭圆
的标准方程;
(2)求证:直线
与
的斜率之积为定值;
(3)判断三点
,
,
是否共线:并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(3)判断三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2022-10-11更新
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1675次组卷
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9卷引用:上海市青浦高级中学2022届高三下学期3月月考数学试题
名校
3 . (1)已知集合
,
.判断集合
与
之间的关系,并证明你的结论;
(2)求证:
是无理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76def8c4445e2c441135a22b0911485f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a074dea3eca933c7ed5dca11cbc37db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
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2020-12-04更新
|
208次组卷
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2卷引用:上海市朱家角中学2021-2022学年高一上学期10月月考数学试题
4 . (1)设
、
,
,求证:
;
(2)请利用二项式定理证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec7e58f57ee4e8667499e3ff9a00ab11.png)
(2)请利用二项式定理证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4fad9318b8c34e067afb27e6cefcc9.png)
您最近一年使用:0次
2020-07-16更新
|
739次组卷
|
8卷引用:上海市复旦大学附属中学青浦分校2022-2023学年高二下学期3月月考数学试题
上海市复旦大学附属中学青浦分校2022-2023学年高二下学期3月月考数学试题上海市静安区2019-2020学年高二下学期期末数学试题(已下线)对点练69 二项式定理-2020-2021年新高考高中数学一轮复习对点练(已下线)专题2.6 排列组合和二项式定理【章节复习专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)(已下线)考向38 二项式定理全归纳(十五大经典题型)-3(已下线)拓展二:二项式定理15种常见考法归类 -【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第三册)(已下线)高二下期末真题精选(易错60题45个考点专练)(高中全部内容)(原卷版)(已下线)第03讲 二项式定理(十五大题型)(讲义)-3
5 . (1)已知双曲线的中心在原点,焦点在x轴上,实轴长为4,渐近线方程为
.求双曲线的标准方程;
(2)过(1)中双曲线上一点P的直线分别交两条渐近于
两点,且P是线段AB的中点,求证:
为常数;
(3)我们知道函数
的图象是由双曲线
的图象逆时针旋转45°得到的,函数
的图象也是双曲线,请尝试写出曲线
的性质(不必证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6bb019e2d7c6d17d15ec4d9043f5e6.png)
(2)过(1)中双曲线上一点P的直线分别交两条渐近于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ec992203c564a3d19669b30f211cf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b6ab702f8e93cc1e680a7d7af06786.png)
(3)我们知道函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00dc461403d9646bee178a26eed24719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5848e50805496263d52dcbde9671a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e952a01fa0e4ab0a4f3ccc40d4ba6e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e952a01fa0e4ab0a4f3ccc40d4ba6e6b.png)
您最近一年使用:0次
名校
6 . 三角比内容丰富,公式很多.若仔细观察,大胆猜想,科学求证,你能发现其中的一些奥秘.请你完成以下问题:
(1)计算:
及
;
(2)根据(1)的计算结果,请你猜想出一个一般性结论,并证明你的结论.
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b07d5408015922c0077f1e1374b583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b0afde62c59484aac3274e7f1fcc8f.png)
(2)根据(1)的计算结果,请你猜想出一个一般性结论,并证明你的结论.
您最近一年使用:0次
2020-01-23更新
|
268次组卷
|
2卷引用:上海市青浦高级中学2016-2017学年高一下学期3月质量检测数学试题
名校
解题方法
7 . 盒子中有5个乒乓球,其中2个次品,3个正品.现从中随机摸取2个小球.
(1)若采用有放回摸球,用
表示摸出的2个小球中次品的个数,求
的分布与数学期望;
(2)若采用不放回摸球,记“第二次摸出的小球是正品”为事件
,求证:
.
(1)若采用有放回摸球,用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)若采用不放回摸球,记“第二次摸出的小球是正品”为事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a009718e6ca1bf47b34b4a30efaea90.png)
您最近一年使用:0次
8 . 已知数列
与
满足
(
为非零常数),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)若
是等差数列,求证:数列
也是等差数列;
(2)若
,
,
,求数列
的前2025项和;
(3)设
,
,
,
,求数列
的最大项和最小项.
![](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/998926638c7b8a50714455fb2c81693b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc578e720c84a0eedc00b06b08f14d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b9d521d0db9cf460c885225c2aa61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0553383350144196c1122a26a188e343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
9 . 已知
、
,设函数
的表达式为
.
(1)设
,
,求函数
在点
处的切线方程;
(2)设
,
,集合
,记
,若
在
上为严格增函数且对
上的任意两个变量s,t,均有
成立,求
的取值范围;
(3)当
,
,
时,记
,其中
为正整数.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f515a2b16232d8c17df0a03a9f835d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68155558673dee3c3b339a73d752097.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4842c7c85e9610baedc948a41107d5e2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0248255c35db564b386e4a997f822a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d2412b086b339e3239162037636102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9a4cae3158b96893800ddc6ebbc76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf80f9cf72a90e6a974a9b634f06887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a915c1a8a9304aeb307d130faaeb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec02c0bae70f3baf4887e1bae8667a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8d30f1878c2512f0418788c564d0e7.png)
您最近一年使用:0次
10 . 若无穷数列
满足:存在正整数
,使得
对一切正整数
成立,则称
是周期为
的周期数列.
(1)若
(其中正整数m为常数,
),判断数列
是否为周期数列,并说明理由;
(2)若
,判断数列
是否为周期数列,并说明理由;
(3)设
是无穷数列,已知
.求证:“存在
,使得
是周期数列”的充要条件是“
是周期数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2b94cbf8f1acc77ed2618d9ba5756a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f195d5a5663e0b1b0870c3f2c39d19dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cff7a7deafe061d63e324c12867f958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b8edc8e215753c36badd65adaee992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc6bb7b937ded40f6f50859d8f77a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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