1 . 已知函数
,且点
处的切线为
.
(1)求
、
的值,并证明:当
时,
成立;
(2)已知
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4edb87617f8dd25e703b7dafdd875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf46dc84732526c826d84a71c407ea89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac2802209e9c013526ef93446d77e5b.png)
(1)求
![](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/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206c6223f53f2291075f407c16fb5d84.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3df3795a62416c1ab5501db40c8206a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7837b7ca9625519a6c7e04930639a38.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,曲线
下有一系列正三角形,设第n个正三角形
(
为坐标原点)的边长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/326e8eff-afba-4a54-904a-1f1520674cfa.png?resizew=166)
(1)求
的值;
(2)求出
的通项公式;
(3)设曲线在点
处的切线斜率为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e03c4f6095c0cd2d0262c738d0b6472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1698b9a76d725f9a254b9798d926fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/326e8eff-afba-4a54-904a-1f1520674cfa.png?resizew=166)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
(2)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(3)设曲线在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbbf4d763f3cbe5a71707bc19c78191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcc0f1666e7fe2b206296984a932deed.png)
您最近一年使用:0次
2024-02-28更新
|
258次组卷
|
2卷引用:河北省石家庄二中2023-2024学年高二上学期期末数学试题
3 . 如果数列
,其中
,对任意正整数
都有
,则称数列
为数列
的“接近数列”.已知数列
为数列
的“接近数列”.
(1)若
,求
的值;
(2)若数列
是等差数列,且公差为
,求证:数列
是等差数列;
(3)若数列
满足
,且
,记数列
的前
项和分别为
,试判断是否存在正整数
,使得
?若存在,请求出正整数
的最小值;若不存在,请说明理由.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56c975b8b3195cea6ef4b9949e5d0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78393519255d80cb3c118a0d71f15511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4719086a4e785f6b5fdb429a313ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f236264ae54f3d8dc03d55c5c9ff88c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c88ebbe7b0f9cd88640b979a874a5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102c6cfe2a85d4dc2450fd082d625f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225c18d9b2d3afe311a2639e3e366249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f50ac3b1d543e1a09eb9e84da4f5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478421b81927e435cbcf5acafa89efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadd9a2715f906b05ad3122c0b2201c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b324005c139eec61bb7b4db496f10e49.png)
您最近一年使用:0次
2024-03-21更新
|
1448次组卷
|
4卷引用:河北省廊坊市香河县第一中学2023-2024学年高三下学期模拟考试数学试卷
河北省廊坊市香河县第一中学2023-2024学年高三下学期模拟考试数学试卷2024届辽宁省高三二模数学试题(已下线)压轴题05数列压轴题15题型汇总-1广东省深圳市深圳高级中学(集团)2024届高三下学期适应性考试数学试卷
名校
4 . 记
为数列
的前
项和,
.
(1)求
和
的通项公式;
(2)设数列
的前
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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e3b3e475fbb609873afb57f1a0186d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e73871e008ea72d24e4e82738c666d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f85c8d9210c7328fbe3d653ffede057.png)
您最近一年使用:0次
2024-04-18更新
|
1402次组卷
|
3卷引用:河北省衡水市枣强县董子学校、秦皇岛市河北昌黎第一中学联考2024届高三下学期4月质量检测数学试题
河北省衡水市枣强县董子学校、秦皇岛市河北昌黎第一中学联考2024届高三下学期4月质量检测数学试题山东省部分学校2023-2024学年高三下学期4月金科大联考(二模)数学试题(已下线)压轴题05数列压轴题15题型汇总-1
名校
解题方法
5 . 已知正项数列
的前n项和为
,且
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d292de307881f3f7835a89ed087b26a.png)
(2)在
与
间插入n个数,使这
个数组成一个公差为
的等差数列,在数列
中是否存在3项
,(其中m,k,p成等差数列)成等比数列?若存在,求出这样的3项,若不存在,请说明理由.
![](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/6e63c6f150443df12cd30ba72043667a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d292de307881f3f7835a89ed087b26a.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7761cc0df6a09d1d7b6749959aecdec4.png)
您最近一年使用:0次
2024-01-10更新
|
960次组卷
|
3卷引用:河北省石家庄市第二十七中学2024届高三上学期金太阳联考数学试题
6 . 已知数列
的前n项和为
,且
,
(
).
(1)证明
是等比数列,并求
的通项公式;
(2)若
,求数列
的前n项和
.
![](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/7def23f30138e0b7c4c1e498d6903a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b69fa8e4172018faebfa39782626e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483eb4433fee05a5810a276433b1742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6fd7a169fb7e25a0f0efe4460b68c8.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
7 . 已知数列
中,
,
,记数列
的前
项的乘积为
,且
.
(1)求数列
的通项公式;
(2)设
,数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aecb726f165cef5a464225d69cef7fc0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c0e0f79f503685fd53eb521763100e.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1f19b7a771a8d1556ed3077688f282.png)
您最近一年使用:0次
2023-04-19更新
|
1991次组卷
|
5卷引用:河北省邯郸市2023届高三二模数学试题
河北省邯郸市2023届高三二模数学试题(已下线)模块六 专题1 易错题目重组卷(河北卷)专题13数列(解答题)重庆市2023届高三下学期5月月度质量检测数学试题(已下线)模块三 专题9 新情境专练 基础 期末终极研习室(高二人教A版)
解题方法
8 . 已知正项数列
满足
,数列
的前n项和为
,且
.
(1)求
的通项公式;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754fab8d21931dadc416bec9d0372322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3802c33d240597aaaa5f8bb7b872a87.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed48c3e5c53eba20c2e262b7d2c09bfc.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10aeff28f50981f5585dfe28d51d5a84.png)
您最近一年使用:0次
2024-02-28更新
|
336次组卷
|
2卷引用:河北省承德市2023-2024学年高二上学期期末数学试题
9 . 已知数列
的前
项和为
,且
.
(1)证明
是等差数列,并求
的通项公式.
(2)对任意正整数
,都有
,且存在常数
,使得
为定值
.设数列
满足
,证明:
.
![](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/73c2a3ac4693f3ec59776987cb84acae.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69eac3188eac59966a17e24fdccdda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5ce81da9e5a476fc572abc576be82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1212d11093fa85bd4b54cc740c5cd4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c10ccc7fbf827004e9043bab8070e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909a8e77c286a4308e92fc1544fb3e69.png)
您最近一年使用:0次
10 . 学校篮球队30名同学按照1,2,…,30号站成一列做传球投篮练习,篮球首先由1号传出,训练规则要求:第
号同学得到球后传给
号同学的概率为
,传给
号同学的概率为
,直到传到第29号(投篮练习)或第30号(投篮练习)时,认定一轮训练结束,已知29号同学投篮命中的概率为
,30号同学投篮命中的概率为
,设传球传到第
号的概率为
.
(1)求
的值;
(2)证明:
是等比数列;
(3)比较29号和30号投篮命中的概率大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96cf3cca9ea974fd60eac45617be8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d1606ed2028310015da998702edd107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8b45edad1f59a7454739675fd2de55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3d61e275223b5a61538859cb38d348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1dd362f843e640ce551ad1787c9873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1dd362f843e640ce551ad1787c9873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b4a54bd0a036c8f79f155c36f51e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051131b840ca5d404df9fe06b21be835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b19c7d44a1829393d1a8ce208a7140.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b65de6aa66b6ead5a3652f1758e3f8.png)
(3)比较29号和30号投篮命中的概率大小.
您最近一年使用:0次
2022-10-17更新
|
2116次组卷
|
7卷引用:河北省衡水中学2022-2023学年高三三调考试数学试题
河北省衡水中学2022-2023学年高三三调考试数学试题山东省潍坊市2022-2023学年高三上学期10月优生抽测数学试题浙江省金华第一中学领军班2022-2023学年高二上学期10月月考数学试题(已下线)专题42 概率与统计的综合应用-3(已下线)数学(乙卷理科)(已下线)模块八 专题10 以概率与统计为背景的压轴大题(已下线)专题9-1 概率与统计及分布列归类(理)(讲+练)-2