名校
1 . 已知
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb96f39637da70f64bb06f0b4a5eb301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba85a9e0c7ecc82a5ad498e3c2c6ab9.png)
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2023-12-14更新
|
110次组卷
|
9卷引用:河南省济源市英才学校2022-2023学年高二下学期期中考试数学试题
河南省济源市英才学校2022-2023学年高二下学期期中考试数学试题2015-2016年北大附中河南分校高二宏志班上抽考文数学卷河南省周口市中英文学校2019-2020学年高二下学期期中考试(6月)数学(文)试题(已下线)考点64 证明(讲解)-2021年高考数学复习一轮复习笔记(已下线)专题12不等式的证明技巧的求解策略解题模板安徽省宿州市泗县第一中学2020-2021学年高二下学期第二次月考数学(理)试题安徽省宿州市泗县第一中学2020-2021学年高二下学期第二次月考数学(文)试题(已下线)2.1 (分层练)用不等式(组)表示不等关系-2021-2022学年高中数学必修第一册课时解读与训练(人教A版2019)(已下线)第12题 综合法由因导果,分析法执果索因(优质好题一题多解)
名校
2 . 已知
是无穷数列,
,
,且对于
中任意两项
,
,在
中都存在一项
,使得
.
(1)若
,
,求
;
(2)若
,求证:数列
中有无穷多项为0;
(3)若
,求数列
的通项公式.
![](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/a55ef34345210312db273ab4981c40f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0616dca5cf0229b9f801365cc2bcfff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba50a82a53f0e597c096ccf5746f1b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53abaaac2e62f510d996e6db22aefe7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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3 . 用反证法证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d89e1f97be2138775f85733e9756e3.png)
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名校
4 . 用反证法证明“平面四边形中至少有一个内角不超过
”,下列假设中正确的是
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
![](https://img.xkw.com/dksih/QBM/2023/9/12/3323438696136704/3323787648319488/STEM/41596727ff834853bcc8a96ce900e371.png?resizew=4)
A.假设有两个内角超过![]() | B.假设四个内角均超过![]() |
C.假设至多有两个内角超过![]() | D.假设有三个内角超过![]() |
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2023-09-13更新
|
564次组卷
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8卷引用:宁夏银川市宁夏育才中学2022-2023学年高二下学期3月月考数学(文)试题
5 . (1)若
,证明:
.
(2)已知
,
,
,
,试证明a,b,c至少有一个不小于1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b162ff5b8a1ca4b0e934dbb1b2fed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3513efc9a14792e1fe9fa3ff5888d396.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab560cdc1f2fff8483e64235774d2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512670a2a8ffebb9ca69d4b75ec16de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033e0d9d0fcdfde98da36c30556ce240.png)
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名校
6 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.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/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
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2023-07-17更新
|
566次组卷
|
5卷引用:北京市顺义区2022-2023学年高一下学期期末质量监测数学试题
北京市顺义区2022-2023学年高一下学期期末质量监测数学试题重庆市南开中学校2023-2024学年高一上学期开学考试数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
7 . 已知
,且
,求证:
和
至少有一个大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797b15e65ad1ed9116eb51764a2b8b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d2a320b9ff137ce3632296c4b1d79a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58a60f2bfac8c6f348ffdeb2b81a0fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0aae6e56e3fd8f0a9b0c9c9ab7ac0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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解题方法
8 . 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)
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2023-03-16更新
|
643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)
解题方法
9 . 试问函数
是否为周期函数?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d71f56ef6906bc37ca312051d97d4c.png)
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10 . 回答下列问题
(1)已知
都是非零实数,且
,求证:
的充要条件是
.
(2)设
,且
,
,
,用反证法证明:
至少有一个大于0.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b21208364124b5c477b2ff8df1c2e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc539c71b72aff71e7c8e31e74969d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c328c9c4ec69c4275e27576fb61655.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b97ab3b66712c79b788f21ec005e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be4763ac99b71f7d741495e103f9eb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f658aef82183d509edd0078236b77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7566946bb9631effbd92fa228477c550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
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