1 . 古希腊数学家欧几里得所著《几何原本》中的“几何代数法”,很多代数公理、定理都能够通过图形实现证明,并称之为“无字证明”如图,
为线段
中点,
为
上的一点以
为直径作半圆,过点
作
的垂线,交半圆于
.连接
,
,
,过点
作
的垂线,垂足为
.设
,
,则图中线段
,线段
,线段______
;由该图形可以得出
,
,
的大小关系为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3d296e0d7154a170cb7d3ae42989b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bcccda6e75578c160552bcb1d7f160b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ce2f12cd473b0877cb01872ec45141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a24490af6cdebc539613da0a98d762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26234bb9c659eb48da0247dd6a465d65.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://img.xkw.com/dksih/QBM/editorImg/2023/11/15/3757da65-71fc-4c20-9430-975b3469b269.png?resizew=185)
您最近一年使用:0次
解题方法
2 . (1)设
,比较
与
的大小关系并证明.
(2)已知
,
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9241861853f8a6300959c0bd5d2da263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a070d6518b58512d61fcb24e889a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fe98cf9536674e3163933cbcc1b994.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/3f3c4af3b4a23d8d7e5fd926a32c5d17.png)
您最近一年使用:0次
3 . 已知数列
满足
,
.
(1)证明:数列
是等比数列;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510fdcb4d1398c334fa619f1dd87b6ba.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc71a2fd8c6b263feea5ff5d6a36121.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec783bca4d43c17bfbad1bb85b094f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2023-11-15更新
|
1319次组卷
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3卷引用:辽宁部分学校2023-2024学年高三上学期期中大联考数学试题
解题方法
4 . 已知正数a,b满足
;
(1)求ab的最大值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0d34836cf6d21bcadd4f60793ba150.png)
(1)求ab的最大值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296a77a7ca3e70fba643654bf5a99a3b.png)
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2023-10-12更新
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354次组卷
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5卷引用:辽宁省县级重点高中联合体2023-2024学年高一上学期10月联考数学试题
名校
解题方法
5 . 设数列
的各项都为正数,且
.
(1)证明数列
为等差数列;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52f9212238a366d3cda80a6b4032a66.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30136113176ba7fe660e998d0873157.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db850e54a545598c4ea061aa6aed9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-09-30更新
|
2611次组卷
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9卷引用:辽宁省六校协作体2024届高三上学期期中联考数学试题
辽宁省六校协作体2024届高三上学期期中联考数学试题(已下线)广东省广州市第九十七中学2024届高三上学期10月月考数学试题甘肃省兰州市教育局第四片区联考2023-2024学年高二上学期期中考试数学试题(已下线)第4章 数列单元检测(基础卷)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)福建省诏安县桥东中学2022-2023学年高二上学期期中考试数学试题(已下线)第4章 数列 章末题型归纳总结(2)(已下线)第09讲 第四章 数列 章节验收测评卷(综合卷)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)(已下线)热点5-1 等差数列的通项及前n项和(8题型+满分技巧+限时检测)(已下线)4.2.2 等差数列的前n项和公式——随堂检测
解题方法
6 . (1)已知______,试比较M,N的大小.从下列两个条件中选择其中一个填入横线中,并解答问题.
①
,
,②
,
.
(2)若
,证明:
.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c8279b4d5ab7bd609dd93ec6a6f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e676cb18451a57de7f796366178eabfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e2813be505811d244989063275115e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a26798d30978791b8c7efd098fd39d4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d229cbec798c9c278a9b5979cb38247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c860e0ac9cab0f5f4b636eff55d1c3.png)
您最近一年使用:0次
7 . 已知数列
满足
.
(1)求证:
为等比数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2b1b047578ffab15bbf453e1879582.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7d94406136605c5bc9cd9295d6c9fa.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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2023-12-07更新
|
1701次组卷
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3卷引用:辽宁省名校联盟2024届高三上学期12月联合考试数学试题
8 . 已知数列
满足
,且
.
(1)证明:
是等比数列,并求
的通项公式;
(2)记数列
满足
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa0802487a22c31a55d372132a3bcf3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483eb4433fee05a5810a276433b1742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a72b757eb5d176c4c9611a4f3051bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
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2023-05-20更新
|
902次组卷
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2卷引用:辽宁省辽东区域教育科研共同体2022-2023学年高二下学期期中考试数学试题
名校
解题方法
9 . 在△ABC中,角A,B,C的对边分别为a,b,c,已知
.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab29f045e046a3698624d6cf19de7e6f.png)
(2)若
,
,求△ABC的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b626c78057d7e0a8704f147e1ebf3c2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab29f045e046a3698624d6cf19de7e6f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e899c486dc49e560fc4aca05e16835b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fa79a550591eb9e1bd07bced3a08fc.png)
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2023-04-30更新
|
2277次组卷
|
14卷引用:辽宁省辽阳市2023届高三二模数学试题
辽宁省辽阳市2023届高三二模数学试题四川省资阳市2023届高考适应性考试数学(理科)试题四川省资阳市2023届高考适应性考试数学(文科)试题贵州省2023届高三下学期联合考试数学(理)试题(已下线)专题1 平面向量(3)江苏省盐城市五校2022-2023学年高一下学期5月联考数学试题(已下线)专题2 平面向量(2)(已下线)模块一 专题3 解三角形(苏教版)云南省楚雄彝族自治州民族中学2022-2023学年高二下学期6月月考数学试题广东省深圳市南方科技大学附属中学2022-2023学年高二下学期期中数学试题(已下线)专题08 解三角形-1四川省泸县第一中学2023-2024学年高三上学期10月月考数学(文)试题四川省泸县第一中学2023-2024学年高三上学期10月月考数学(理)试题(已下线)模块一 专题4 三角函数与解三角形(人教A)3
名校
解题方法
10 .
为数列
的前
项和,已知
,
.
(1)求证:数列
为等差数列;
(2)设
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61cc942eaa2c2d9f47608ddfcdd716c.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216876de04325fd250c38c485cbc34b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-06-19更新
|
1196次组卷
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3卷引用:辽宁省沈阳市新民市高级中学2022-2023学年高二下学期6月月考数学试题