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
解题方法
2 . 设数列
的前
项和为
,若
.
(Ⅰ)证明
为等比数列并求数列
的通项公式;
(Ⅱ)设
,数列
的前
项和为
,求
;
(Ⅲ)求证:
.
![](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/9ca9605501cceb252348510d860f07c7.png)
(Ⅰ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b008e35e4367db818d464d31bd2248c.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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(Ⅲ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfc690ace28306596f1fa5c88fa3c3d.png)
您最近一年使用:0次
2020-12-14更新
|
2192次组卷
|
8卷引用:河南省南阳市邓州春雨国文学校2022-2023学年高二下学期3月考试数学试题
河南省南阳市邓州春雨国文学校2022-2023学年高二下学期3月考试数学试题上海师范大学附属中学闵行分校2023-2024学年高二上学期期中数学试题浙江省强基联盟2020-2021学年高二上学期期中数学试题(已下线)【新东方】415(已下线)专题08 数列的通项、求和及综合应用 第一篇 热点、难点突破篇(讲)-2021年高考数学二轮复习讲练测(浙江专用)(已下线)专题4.3 等比数列(B卷提升篇)-2020-2021学年高二数学选择性必修第二册同步单元AB卷(新教材人教A版,浙江专用)(已下线)第4章 等比数列(A卷·夯实基础)-2021-2022学年高二数学同步单元AB卷(苏教版2019选择性必修第一册)【学科网名师堂】(已下线)专题08 数列的通项、求和及综合应用(讲)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(浙江专用)》
解题方法
3 . 已知数列
满足:
.
(1)证明:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb11f8d571702101e97df5dfa8040249.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ef5fc9014e6fae3aae9da1b32db744.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba90fa7ea3d33afe86227e3cbcabe119.png)
您最近一年使用:0次
11-12高三下·北京朝阳·阶段练习
4 . 已知各项均为非负整数的数列
,
,
,
,满足
,
.若存在最小的正整数
,使得
,则可定义变换
,变换
将数列
变为
,
,
,
,0,
,
,
.设
,
,1,
.
(1)若数列
,1,1,3,0,0,试写出数列
;若数列
,0,0,0,0,试写出数列
;
(2)证明存在数列
,经过有限次
变换,可将数列
变为数列
;
(3)若数列
经过有限次
变换,可变为数列
.设
,
,2,
,
,求证
,其中
表示不超过
的最大整数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae042263f3b7ce512320a7148baa724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c996bcd14149792beddc817232d5223d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c8d0474f7d81ef8dbefaacfd5afe7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e4d07536ef32771e2f7b663d778661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d16bad5d7d2a0683654b8bca4b0b1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cfd90034be27bd549bff6ba9f3711cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77311d40ef50a900cb46680f917f0d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f974ab6b958a752f8676150487831cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63abc00fb752da8d6261f4d9c7f8a868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1487f4b936e5f924fa6b1ea298e302f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5cfdde9c6d1b8bb15b7bb506c30ca8.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc12e4a7c5419c166a1fdc0ae55eda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a44ad5355d0e43ad9a1b8ec74373c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
(2)证明存在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d144544bd6df279514d7e8483fbb1c.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d144544bd6df279514d7e8483fbb1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23819fa1ef78b4a00c2231390ccc3245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882abcce3accf2293e9976b054e92d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6f9256cd0df49c36951818db959695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40da12b68a6b48910028c49657f160bd.png)
您最近一年使用:0次
5 . 已知数列
的前n项和
,数列
满足:
,
.
(1)证明:
是等比数列;
(2)设数列
的前
项和为
,且
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设数列
满足:
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5886e031a95a8d52c9306e6b1c518abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06561e5778ee1b9dafdd587539b870d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921439ba032dd3fdec48755411b04533.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.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/d59800cfb8b87374c03bf3a04b0fd586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2303ba9889cabc817bf05eb0eca57fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8273a6fb20d688b3f5d7faf3fc352bca.png)
您最近一年使用:0次
6 . 设函数
.
(1)讨论函数
的单调性.
(2)设数列
满足
,证明:数列是单调递增数列,且
,
(其中
为自然对数的底).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436d89f98040d869c912b9193dbbdd45.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83271e8ed836063e7c3ff9f535a7dc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c408d00eb43d6350af01b2d43dd8b283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
您最近一年使用:0次
2023-12-16更新
|
396次组卷
|
3卷引用:安徽省“皖江名校联盟”2024届高三上学期12月月考数学试题
名校
解题方法
7 . 设数列
的前n项和为
,已知
,
.
(1)证明数列
为等比数列;
(2)设数列
的前n项积为
,若
对任意
恒成立,求整数
的最大值.
![](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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a00d92524667782ed663ff3d92e720c.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68223e959d7b55d4b4f30d94059b69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-12-13更新
|
911次组卷
|
4卷引用:江苏省百校大联考2024届高三上学期第二次考试数学试题
名校
解题方法
8 . 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
|
962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
解题方法
9 . 记
为数列
的前
项和,已知
,
.
(1)求
的通项公式;
(2)令
,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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6b7eeda1ca25d1630e3eca48061c7d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053d545d85e8e4b7f96e41500efd6945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3593087fb880597ad563d015c7027ca.png)
您最近一年使用:0次
解题方法
10 . 已知数列
的前n项和为
,且
.
(1)求
;
(2)若
,记数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498c96b078ab1ded4bdda837f83a3450.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438591068dee340b57be6d3f2b7fc70e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11dee498fc0e363bc1e79a1ce52dcd92.png)
您最近一年使用:0次