名校
解题方法
1 . 已知数列
中,
,其前n项和为
,
.
(1)求数列
的通项公式;
(2)设
,若数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f1c9bdfb252a71b1fc88d7f8082240.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5214360ac0152818f5b95b805f6e615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50048f2ab3c89aa1dd2ddb75df35b47f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c215db1d8f69757118ad405b78035628.png)
您最近一年使用:0次
2022-10-29更新
|
672次组卷
|
4卷引用:吉林省通化市辉南县第六中学2022-2023学年高二上学期期中数学试题
吉林省通化市辉南县第六中学2022-2023学年高二上学期期中数学试题湖南省郴州市2022-2023学年高三上学期第一次教学质量监测数学试题江苏省南京市第一中学2022-2023学年高三上学期9月质量检测数学试题(已下线)4.3.1 等比数列的概念(第2课时)(分层作业)-【上好课】2022-2023学年高二数学同步备课系列(人教A版2019选择性必修第二册)
名校
解题方法
2 . 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
名校
解题方法
3 . 已知各项均为正数的数列
的前
项和为
,且
,
,
成等差数列.
(1)证明:数列
是等比数列,并写出数列
的通项公式;
(2)若
,设
,求数列
的前
项和
.
![](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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b0f4c4bb231801fc88b28f05c10ec8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.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
4 . 已知数列
满足
,设
.
(1)证明:
是等比数列;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df513f2474585198bb450595009a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccfff8a536dfc150e13a700b9d3e3d3.png)
您最近一年使用:0次
2022-09-06更新
|
866次组卷
|
5卷引用:吉林省吉林市普通高中友好学校2022-2023学年高二上学期期末联考数学试题
吉林省吉林市普通高中友好学校2022-2023学年高二上学期期末联考数学试题河南省杞县高中2022-2023学年高三上学期开学联考文科数学试题(已下线)第04讲 数列求和(练)甘肃省金昌市永昌县第一高级中学2022-2023学年高三上学期第一次模拟考试数学(文)试题(已下线)第7讲 数列求和9种常见题型总结 (1)
名校
5 . 已知函数
和
有相同的最大值,并且
.
(1)求
;
(2)证明:存在直线
,其与两条曲线
和
共有三个不同的交点,且从左到右的三个交点的横坐标成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd47d14455dfe82e80cef3515203e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b56fd7d7082666f4e2f539af26f207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f47d0bdb7d49fb3961b578cfd00576.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)证明:存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead6a3dbd03539ef5e0807be57bb1e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
6 . 在数列
中,
,
,
.
(1)求证:
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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a76fc5c4b88789bdcdd0825765bc4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17d72d1d20d385920c3d9da6bed8bb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843da340a59e62fab3809cf79dec4f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da72309d2507e2f5e5ed88d8cc08963.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
2022-06-10更新
|
787次组卷
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4卷引用:吉林省白城市通榆县毓才高级中学2023-2024学年高三上学期9月月考数学试题
名校
解题方法
7 . 已知数列{an}(n∈N*)是公差不为0的等差数列,a1=1,且
,
,
成等比数列.
(1)求数列{an}的通项公式;
(2)设数列{
}的前n项和为Tn,求证:Tn<1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14771ad8f9fd441429ba43bf00ec794e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab0ddb0876fafbfb4dd8451f8b38c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221e08845f95c15b3ee8a64fc80ce234.png)
(1)求数列{an}的通项公式;
(2)设数列{
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0d9f8bf8dd91d8cd659ce6fb9c80b8.png)
您最近一年使用:0次
2022-10-20更新
|
372次组卷
|
2卷引用:吉林省长春市第五中学2022-2023学年高二下学期第一学程考试数学试题
2022·全国·模拟预测
名校
解题方法
8 . 已知
为等比数列
的前n项和,若
,
,
成等差数列,且
.
(1)求数列
的通项公式;
(2)若
,且数列
的前n项和为
,证明:
.
![](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/e4b32aee86109b777671cd62868db3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86e2e42b4aa93db9241103e7f61766c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3fc854e1dd70727f12571df8c4a54c9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/716d59cee712c22885b6608848980b75.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/8195c685bcd7d2a14675625beec0d027.png)
您最近一年使用:0次
2022-12-05更新
|
4279次组卷
|
13卷引用:吉林省白山市抚松县第一中学2023届高考模拟预测数学试题
吉林省白山市抚松县第一中学2023届高考模拟预测数学试题吉林省通化市梅河口市第五中学2023-2024学年高三上学期9月月考数学试题(已下线)2023年普通高等学校招生全国统一考试数学领航卷(二)(已下线)专题05 数列放缩(精讲精练)-1云南省昆明市第三中学2023届高三上学期12月月考数学试题(已下线)新高考卷04四川省江油市太白中学2022-2023学年高三下学期高考模拟(三)数学试题山西省山西大学附属中学2024届高三上学期9月月考(总第三次)数学试题四川省眉山市仁寿县仁寿县铧强中学2023-2024学年高三上学期10月月考数学试题四川省眉山市仁寿县铧强中学2023-2024学年高三上学期10月诊断性考试文科数学试题湖南省邵阳市邵东一中2024届高三上学期第四次月考数学试题安徽省淮北市树人高级中学2023-2024学年高二上学期12月阶段测试数学试题福建省龙岩市第一中学2024届高三上学期第三次月考数学试题
名校
解题方法
9 . 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
10 . 已知数列
,
满足
,
,
,
.
(1)求证:
;
(2)求证:
;
(3)设数列
的前n项和为
,求证:
.
![](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/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6d8a8a57db1c2fc7f465d2cfd2aa78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71406c902e2bfb15f5b84ea419611e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5530b78617f9a9976adc605a71fe0d48.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25528980b648e76c63bedf345e95a713.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e970038ed20d95a45c228ee5572861.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362832fa3d3c13c1eafd565349d66dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e637fe1df3fffd9330e03f91626dbce.png)
您最近一年使用:0次