名校
解题方法
1 . 记
的内角A,B,C的对边分别为a,b,c,分别以a,b,c为直径的三个半圆的面积依次为
,
,
.
(1)若
,证明:
;
(2)若
,且
的面积为
,
,求b.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073dd017ec6e41fa8bc105355037010d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f67985b822b482f804d56d5df049f15.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544c8e70d47910c535a4bef844282be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec33b3ab96553ff4d05d26db0c6dfba3.png)
您最近一年使用:0次
名校
解题方法
2 . 已知正项数列
的前n项和为
,
.
(1)求数列
的通项公式;
(2)设
,数列
的前n项和为
,证明:
.
![](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/768c850421989c8a4bccbdaca4e3bc69.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f128819d216f23d0266882fe5b4cb0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d76c3eb0a07a827877d7a4dc306211.png)
您最近一年使用:0次
2023-01-16更新
|
1435次组卷
|
6卷引用:吉林省长春市东北师范大学附属中学2022-2023学年高二下学期期末数学试题
3 . 在△ABC中,内角A,B,C的对边分别为a,b,c.从下面①②③中选取两个作为条件,证明另外一个成立.
①
;②
;③
.
注:若选择不同的组合分别解答,则按第一个解答计分.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765ff3b58624701511f4120b2f48cfca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4c86001d89a2c26844074df7d35a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0f8cec0bda89b6c2ad7ab3cd6c219c.png)
注:若选择不同的组合分别解答,则按第一个解答计分.
您最近一年使用:0次
2023-03-13更新
|
1505次组卷
|
4卷引用:东北三省三校2023届高三第一次联合模拟考试数学试题
(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题东北三省三校2023届高三第一次联合模拟考试数学试题(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题山东省淄博市2023-2024学年高三上学期期中数学试题
名校
解题方法
4 . 已知
为等差数列,公差为d,
是公比为2的等比数列,且
,
.
(1)证明:
;
(2)求集合
的子集个数.
![](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/769fe52ac96348d3b12d23d06d702595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4660b8e4504f8ad6fe504690c8d033.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d38c4c234dd55eaf29979489df6f99b.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b4a71393ca550f45ffc21354ab9cf0.png)
您最近一年使用:0次
5 . 记
为数列
的前
项和,已知
.
(1)证明:
是等差数列;
(2)若
,记
,求数列
的前
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/6f7847150a29eca2f0fccca9a1e72af3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738dc67ac3b150252a964d1ffe3dfa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d9bc2dea229a96bcedd90bfce5ea0c.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2022-12-29更新
|
994次组卷
|
8卷引用:吉林省辽源市第五中学校2022-2023学年高二上学期期末数学试题
吉林省辽源市第五中学校2022-2023学年高二上学期期末数学试题河南省百师联盟2023届高三一轮复习联考(四)全国卷文科数学试题(已下线)广东省深圳市高级中学(集团)2023届高三上学期期末数学试题变式题17-22(已下线)湖南省怀化市2022-2023学年高三上学期期末数学试题变式题17-22山西省晋中市晋中新格伦双语学校等2校2022-2023学年高三上学期12月月考文数试题云南省马关县第一中学2023届高三第七次月考数学试题江西省宜春市丰城第九中学2023届高三下学期重点班开学质量检测数学(文)试题上海市七宝中学2023-2024学年高二上学期期中数学试题
6 . 记
的内角
、
、
的对边分别为
、
、
,已知
.
(1)证明:
;
(2)若
,
,角
的内角平分线与边
交于点
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157d2f0f0db718649f148134436c3a43.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428d8ba5d74557ac0660343e61b3bd8f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9597cc64469c379d47dfc6b3f27feee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
2023-04-07更新
|
2133次组卷
|
3卷引用:吉林省长春市十一高中2022-2023学年高一下学期第二学程考试数学试题
名校
解题方法
7 . 已知数列
为等差数列,
是数列
的前
项和,且
,
,数列
满足
.
(1)求数列
、
的通项公式;
(2)令
,证明:
.
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fcd86b9ed6819116a261629f96fae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cf0e722239dd3c7f44795f74aa6bf4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1796d3b3d59e53a318ced796ebda0538.png)
您最近一年使用:0次
2023-01-18更新
|
760次组卷
|
5卷引用:吉林省通化梅河口市第五中学2021-2022学年高二下学期开学考试数学试题
名校
解题方法
8 . 在数列
中,
.
(1)证明:
是等比数列;
(2)若数列
的前
项和
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a168cd8b429faa0861a23b3ae0a5c04e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)若数列
![](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/195a7ebe10c1ca78d63f16815e130413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-01-16更新
|
660次组卷
|
6卷引用:吉林省白城市通榆县2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 已知数列
的前n项和为
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c599e7cec6d192fb73218e7882ceca.png)
(1)求
的通项公式
(2)求证数列
是等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c599e7cec6d192fb73218e7882ceca.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)求证数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
您最近一年使用:0次
2022-11-28更新
|
1769次组卷
|
8卷引用:吉林省辽源市第五中学校2022-2023学年高二上学期期中数学试题
名校
解题方法
10 . 在
中,角A,B,C所对的边分别为a,b,C,且
.
(1)求证:
;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc59a08ff6146a651115e1209925ccb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5cfb6a83413cffd657eae19813e381.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ba08d1dd82070b1d9245faaa8057e5.png)
您最近一年使用:0次
2022-10-11更新
|
392次组卷
|
7卷引用:2020届吉林省长春市高三质量监测(三)(三模)数学(理)试题
2020届吉林省长春市高三质量监测(三)(三模)数学(理)试题江西省宜春市上高二中2021届高三热身考数学(文)试题(已下线)2022年全国新高考Ⅰ卷数学试题变式题9-12题湖南省长沙市第一中学2021-2022学年高一下学期期末数学试题(已下线)2022年全国新高考Ⅰ卷数学试题变式题17-19题江苏省南京市第二十九中学2022-2023学年高二上学期10月月考数学试题河北省武邑中学2023-2024学年高三上学期1月期末考试数学试题