1 . 已知各项均不为0的数列
满足
(
是正整数),
,定义函数
,
是自然对数的底数.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)记函数
,其中
.
(i)证明:对任意
,
;
(ii)数列
满足
,设
为数列
的前
项和.数列
的极限的严格定义为:若存在一个常数
,使得对任意给定的正实数
(不论它多么小),总存在正整数m满足:当
时,恒有
成立,则称
为数列
的极限.试根据以上定义求出数列
的极限
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bf7b5dc247fe10b6bfd984413a5e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd9ea8ffdea8c77370ea3e5f563dc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fec2729d8e927de9392ee90d1e0389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6f0a55fa53bf5f8e6654897975bcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3324481138f2dc750f9ad889054abe1.png)
(i)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416a72de4d0030203a867cc3b7b95d83.png)
(ii)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0857559ed421cc7c614708f34f9f3324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9de1835c164233db8b623489fbda0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
解题方法
2 . 已知
为非常数数列且
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a62ab68e3f500af2cc509bd733c0b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1292b689ae033d201118a390676a9747.png)
A.对任意的![]() ![]() |
B.对任意的正数![]() ![]() ![]() ![]() |
C.不存在![]() ![]() ![]() |
D.不存在![]() ![]() |
您最近一年使用:0次
解题方法
3 . 已知数列
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819d72974cc2440af9a448e5076246a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794dd235c980222337d01626c96371f9.png)
A.对任意的![]() ![]() ![]() |
B.对任意的![]() ![]() ![]() |
C.对任意的![]() ![]() ![]() |
D.对任意的![]() ![]() ![]() |
您最近一年使用:0次
2022-01-03更新
|
1138次组卷
|
5卷引用:浙江省绍兴市诸暨市海亮高级中学2021-2022学年高三上学期12月选考数学试题
浙江省绍兴市诸暨市海亮高级中学2021-2022学年高三上学期12月选考数学试题浙江省绍兴市诸暨市海亮高级中学2022届高三下学期高考前最后一卷数学试题(已下线)专题6-1 数列函数性质与不等式放缩(讲+练)-2(已下线)专题9 周期数列 微点2 周期数列的“脸谱”识别(已下线)第4章 数列 章末题型归纳总结(3)
4 . 对任意
,函数
满足
,
,数列
的前15项和为
,数列
满足
,若数列
的前
项和的极限存在,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5621a6b6ddbd6412ec54095f3ee99667.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbf139cb950fd2d25e244a2e4b2e934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb2941a43e3279928cf9aa59b13d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc2d5ea44c605de2d85d0f654cc5d79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01347a3f2ff07802ff713dd7827482d0.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/5621a6b6ddbd6412ec54095f3ee99667.png)
您最近一年使用:0次
2022-11-28更新
|
994次组卷
|
2卷引用:上海市实验学校2023届高三上学期11月月考数学试题
5 . 对于数列
,若
是关于
的方程
的两个根,且
,则数列
所有项的和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d514eb8dff80d4dc3f39de516b63b846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cede7b90e49fca9069a92c36fdc5d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2022-09-11更新
|
818次组卷
|
4卷引用:专题4求和运算 (提升版)
(已下线)专题4求和运算 (提升版)上海市虹口区2021-2022学年高二下学期期末在线测试数学试题福建省宁德第一中学2022-2023学年高二上学期9月月考(一)数学试题(已下线)4.2 等比数列的前n项和(第2课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020选择性必修第一册)
6 . 与大家熟悉的黄金分割相类似的还有一个白银分割,比如A4纸中就包含着白银分割率.若一个数列从0和1开始,以后每一个数都是前面的数的两倍加上再前面的数:0,1,2,5,12,29,70,169,408,985,2378,…,则随着n趋于无穷大,其前一项与后一项的比值越来越接近白银分割率.记该数列为,其前n项和为
,则下列结论正确的是( )
A.![]() ![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
7 . 设数列
满足
,证明:
存在且等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21296826c9f4a87c6355009da1738456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb3a970bf38d5616614fbc065edee88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
8 . 已知函数
的图象是自原点出发的一条折线,当
(
)时,该图象是斜率为
的线段,其中常数
且
,数列
由
(
)定义.
(1)若
,求
,
;
(2)求
的表达式及
的解析式(不必求
的定义域);
(3)当
时,求
的定义域,并证明
的图象与
的图象没有横坐标大于1的公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed2be63fc4c8ab5ad34817459fe7e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6961967d7e48061a9cbb14f597e73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8212e307836cb33f16575e23f6b808e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406185f4ad8bcd99e23adc8d289088ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04a87082c00feca63aaea95a41f30d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6961967d7e48061a9cbb14f597e73d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bdc8d2686a05f12a2ba8a7e3b01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
您最近一年使用:0次
解题方法
9 . 如图所示,
,
,…,
,…是曲线
(
)上的点,
,
,…,
,…是x轴正半轴上的点,且
,
,…,
,…均为等腰直角三角形(
为坐标原点).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1ffc8f62-96ab-455a-9972-4df3009665de.png?resizew=238)
(1)求数列
的通项公式;
(2)设
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c051c2459ca7e2edd8ece9e565ec4b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af2d78b119739a1242e1ae274a9198a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc65d6eb9b63f96d80b54ec9893aee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2326cb86431ec57dededd7c9ed60a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba15787e7f3851a3f24936000212296e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b25286f6029da66ce5270aacd05184f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f097e3c2591eeae50ba0d92b984d625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add8209d60d4bb35d09a0338d3e5e165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6696f67db73ba4a3eca968af0323f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1ffc8f62-96ab-455a-9972-4df3009665de.png?resizew=238)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a388dd60ad00d4874a9af61a1d09f054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2021-09-25更新
|
554次组卷
|
2卷引用:高中数学解题兵法 第一百十二讲 归纳、猜想
10 . 已知
表示不小于
的最小整数,例如
.
(1)设
,
,若
,求实数
的取值范围;
(2)设
,
在区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d45335f199dd5cf7e6a983a4110ead.png)
上的值域为
,集合
中元素的个数为
,求证:
;
(3)设
(
),
,若对于
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d60d72b51085ff7074db4052a867df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28a3002b619eb45f43ddd7f80af1d62.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3649d731e13efb44ebcd880f5fe45491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838b7964f9253718937399d087b061ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f1ba0a1129741502600e47bf058c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f86cbe53a0d1c57ec6875c3bda0224e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d45335f199dd5cf7e6a983a4110ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31eb761dbf1a5a1106dad1a25ce08a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a940fb552e971bc2d56920ab1931704c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93086b41db64fef24e09e0ca5fac715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f04a01f96738e961084100ed412722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057f214e6d3bd8beb020c7a667d97811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e8f7120bfaf3ff3a6c5564ed826769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-02-02更新
|
782次组卷
|
2卷引用:上海市十三校2016届高三下学期3月联考(理)数学试题