1 . (1)设
,
,
,用综合法证明:
;
(2)已知
,
,且
,用反证法证明:
和
中至少有一个小于2.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbefc06b3b4e54a6a1690e870efc69b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bbd0aae5a4f6129fc78f88f662f092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165b2250624fc1f1551d6c38991487d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb82093f9c1ec3ee4218ae8f8377644.png)
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2 . 已知
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a7e7ca61f9605b0d309923e3a64762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4bf6cfdcec4b466f4d60ffa37527e05.png)
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2023高三·全国·专题练习
3 . 设
,给定数列
,其中
,
,
.证明:
(1)
.
(2)如果
,那么当
时,必有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](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/75ab998a5e347af02ca52d29ced30940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87de3864d9d0ce93638a99b87590f3b.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dfdac83e7aaac092e7e7a4e91a2e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e29d198c2f468ff2309d420b89667e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0e11a36f78b6ec85fa8ddb95c7beba.png)
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4 . 设
.
(1)若
,证明:
;
(2)已知
,
且
,用分析法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114b1d85a3f52a2959c49ec25630dfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec307143b4bf45106369f256a796d61.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4dcc5d823c113fcd61c4b7e9639a5a9.png)
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2023高三·全国·专题练习
5 . 设
是一个自然数,
是
的各位数字的平方和,定义数列
:
是自然数,
(
,
).
(1)求
,
;
(2)若
,求证:
;
(3)求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3bf2007903adc64d089a054c2284a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13ee40e6cfa757f60396a5a93202c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1505d56f0b35fe7f2de1fe1888036e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621d38cb93dceb8487ff64a7c4d1c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f06aef3197f50d50505ab596dc31620.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592871252c561ff04cf055064822eaa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ade3a1d01605706801e238726e55fb.png)
(3)求证:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1741807e6cd730f285abd967f4bea5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742a31e28de9309da5f9ef176a1c24fd.png)
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6 . 设
.
(1)
,证明:
;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114b1d85a3f52a2959c49ec25630dfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec307143b4bf45106369f256a796d61.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2504fe7020ff898ca5955a423bed0096.png)
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名校
解题方法
7 . (1)已知
都是正实数,求证:
.
(2)设
,且
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef3052cd1be7641eb559c5d7ed142cb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff6d61a8eaff20b364a9e3235577c69.png)
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名校
解题方法
8 . (1)已知b克糖水中含有a克糖
,再添加m克糖
(假设全部溶解),糖水变甜了.我们将这一事实表示为不等式:当
时,有
,请证明这个不等式;
(2)设
的三边长分别为
,请利用第(1)问已证不等式证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d49655ebe52ed0e7561f0da99cbe9fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111f948bc9a44eef670a04f31e4dedd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0ba96a400a4c158eefc9648b0c130c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c16171f1f79d33dbdf4e2dc280b16943.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13a05f5aca98574bb1f927123490de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f4233a7afad30d1ae8f8cda1901a9e.png)
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2022-10-23更新
|
270次组卷
|
5卷引用:陕西省西安市鄠邑区2022-2023学年高二下学期期中模拟理科数学试题
陕西省西安市鄠邑区2022-2023学年高二下学期期中模拟理科数学试题福建省莆田第一中学、擢英中学2023-2024学年高一上学期10月月考数学试题(已下线)第二章 一元二次函数、方程和不等式单元复习提升-速记·巧练(人教A版2019必修第一册)云南省昆明市第八中学2023-2024学年高一上学期12月月考数学试题四川省眉山市彭山区第一中学2022-2023学年高一上学期10月月考数学试题
9 . (1)设
,证明:
;
(2)已知
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9185519a1b1928d6cd4147f43c738145.png)
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2022-09-15更新
|
188次组卷
|
2卷引用:广西南宁市第二中学2023-2024学年高一上学期第一次大测(一)(10月月考)数学试题
10 . 已知
,
.请选择适当的方法证明.
(1)若
,证明:
;
(2)若
,证明:
与
不能同时成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98941347dd7ac01f5e63a6c5930dd5fa.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656cacf9b32ce8f718dcb50bc8994593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f678dde8a2f44b8eae985b11bf4b50.png)
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2022-05-05更新
|
285次组卷
|
3卷引用:专题04常用逻辑用语-【倍速学习法】(沪教版2020必修第一册)
(已下线)专题04常用逻辑用语-【倍速学习法】(沪教版2020必修第一册)河南省商丘市商丘名校2021-2022学年高二下学期期中联考数学理科试题上海市七宝中学2022-2023学年高一上学期10月月考数学试题