名校
解题方法
1 . 数列
中,
,
,若不等式
恒成立,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f76978d852aee03bf476431750254f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea420b13d5873ed8402bc42e6bc69ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-05-02更新
|
981次组卷
|
4卷引用:2019届豫科名校大联考高三模拟数学(理科)试题
2019届豫科名校大联考高三模拟数学(理科)试题重庆市育才中学2020-2021学年高二上学期10月月考数学试题(已下线)专题5-1 均值不等式及其应用归类(讲+练)-2(已下线)【练】 专题2 构造数列问题
2 . 已知公差不为零的等差数列
中,
,
成等比数列.
(1)求数列
的通项公式;
(2)若数列
满足
,
,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/edcd9a1492c60152f2e32604cd519e72.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503493f08a14baf61394dae4f17240a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80d391ce75d5734c5f9dad385140230.png)
您最近一年使用:0次
3 . 已知数列
是等比数列,且满足
,
是数列
的前
项和,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592f303f546159026b7073f6fa3de23a.png)
,
.
(1)求
,
的通项公式;
(2)设
,
是数列
的前
项和.若对任意的正整数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fbbe714dcd2d5d58cba3c83b6df1260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b250e4276bf3f328b03a66765541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592f303f546159026b7073f6fa3de23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbabab060a644ef97510d98f6337be30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abc949d8bf8f13d2ff6aed6d88fbe1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7620204ef2380d9016d4f8da21c7ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b250e4276bf3f328b03a66765541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b250e4276bf3f328b03a66765541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60fe386994d92b31ad9cc3301dacf1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-03-31更新
|
531次组卷
|
2卷引用:2020届浙江省嘉兴市第一中学高三上学期期中数学试题
名校
解题方法
4 . 数列
分别满足:
,其中
,其中
,设数列
前n项和分别为
.
(1)若数列
为递增数列,求数列
的通项公式;
(2)若数列
满足:存在唯一的正整数k(
),使得
,则称
为“k坠点数列”
(Ⅰ)若数列
为“6坠点数列",求
;
(Ⅱ)若数列
为“5坠点数列”,是否存在“p坠点数列”
,使得
,若存在,求正整数m的最大值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccac8d4bf94ea8cdfc3ff978b7947be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c771a7a0d86420812d759c8b309a7a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478421b81927e435cbcf5acafa89efd7.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525609ab749dd7fd7318cecba5ce0745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(Ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(Ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45a4a72bdca2a17b689b34387e816d8.png)
您最近一年使用:0次
5 . 已知数列
的前
项和为
,且
,
.
(1)若数列
是等差数列,且
,求实数
的值;
(2)若数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e35ba37b0cc1d390e05391554e9660.png)
,且
,求证:数列
是等差数列;
(3)设数列
是等比数列,试探究当正实数
满足什么条件时,数列
具有如下性质
:对于任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
,都存在
使得
,写出你的探求过程,并求出满足条件的正实数
的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f108d4cbb79fbc793f2dfc9209b9436d.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b24e22503480d88ec847c9bc1be5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e35ba37b0cc1d390e05391554e9660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d307ec71820b6536453fbdb5069da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e47ad8ce86152a6e9e3dd0c1c0b08e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d307ec71820b6536453fbdb5069da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a285296b1a05924eeb644c09a0b4282d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-03-24更新
|
816次组卷
|
8卷引用:2019年上海市长宁(嘉定)区高三上学期期末质量检测(一模)数学试题
2019年上海市长宁(嘉定)区高三上学期期末质量检测(一模)数学试题2019年上海市长宁区、嘉定区高三上学期期末教学质量检测(一模)数学试题北京一零一中学2019-2020学年度第二学期高三数学统练(二)(已下线)强化卷05(3月)-冲刺2020高考数学之少丢分题目强化卷(山东专版)(已下线)专题01 拿高分题目强化卷(第三篇)-备战2021年新高考数学分层强化训练(北京专版)江苏省常州市前黄高级中学2020-2021学年高三上学期期中适应性考试数学试题上海海洋大学附属大团高级中学2023届高三上学期一模数学试题(已下线)专题17 数列探索型、存在型问题的解法 微点3 数列探索型、存在型问题综合训练
名校
解题方法
6 . 记
为等比数列
的前n项和,已知
,
.
(1)求
的通项公式
(2)求
;
(3)判断
,
,
是否成等差数列,若是,写出证明过程;若不是,说明理由.
![](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/9a0bf1ebce75e828fd999cc04a319502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dfe5b322577f02fd19caab8cf20170.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebadf2b3ec3dc92cd902eff76085ad46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a35d79a1b4df9e4aade6a92f35bea2.png)
您最近一年使用:0次
2020-03-04更新
|
288次组卷
|
2卷引用:2020届湖南省衡阳市第八中学高三上学期第六次月考数学(文)试题
7 . 从数列
中取出部分项组成的数列称为数列
的“子数列”.
(1)若等差数列
的公差
,其子数列
恰为等比数列,其中
,
,
,求
;
(2)若
,
,判断数列
是否为
的“子数列”,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec07a126ada2c921c5b4337f77854cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaa992a449b828df0ff545e233b279b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84f592310f4b9637b225cab622b2aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d438131add92b51c4e0b06ec6aff581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373ecb5531c1593f13a0ed081597b3cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d38a1171131b1a1f3f70ca2117be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221016d4bfafd5693a4e767fcf6a2559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2019-11-14更新
|
370次组卷
|
3卷引用:上海市闵行区七宝中学2018-2019学年高二下学期开学考试数学试题
上海市闵行区七宝中学2018-2019学年高二下学期开学考试数学试题上海市七宝中学2018-2019学年高二下学期3月月考数学试题(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)
8 . 已知各项都是正数的数列
的前n项和为
,且
,数列
满足
.
(1) 求数列
的通项公式;
(2) 设数列
满足
,求和
;
(3) 是否存在正整数
,使得
成等差数列?若存在,求出所有满足要求的
;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/78515a07797b245e751d0937e2cbb875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f914bc18b8d61d1696ea4f46a23eee.png)
(1) 求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e567d7e9761951a266953c8d5042ac.png)
(2) 设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32cdc06d7684480bec7b86adaaaef111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e5e146226460d8a41162d993789a7a.png)
(3) 是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55336fb58f8e6ea100d0f62390a7265a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c67ea5ac329d33ab3d58a07cdf19b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c5fe8a9ad42e52a8a40242865c6752.png)
您最近一年使用:0次
2020-01-18更新
|
376次组卷
|
5卷引用:江苏省扬州市2017-2018学年度第一学期期末调研测试高三数学试题
江苏省扬州市2017-2018学年度第一学期期末调研测试高三数学试题(已下线)2017-2018学年度下学期高中期末备考 【浙江版】高一【精准复习模拟题】 拔高卷01【教师版】上海市实验学校2017-2018学年高三下学期第五次3月月考数学试题(已下线)专题14 数列的综合应用-《巅峰冲刺2020年高考之二轮专项提升》(江苏)上海师范大学附属中学2021届高三下学期3月月考数学试题
9 . 已知数列
的首项为1.记
.
(1)若
为常数列,求
的值:
(2)若
为公比为2的等比数列,求
的解析式:
(3)是否存在等差数列
,使得
对一切
都成立?若存在,求出数列
的通项公式: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/35cf68967761b8372ce267842682838a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf59c5075f9e6fdf3782b6c0e528237.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
(3)是否存在等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dfea8ec720dcff94cb09798d85d6e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2019-09-23更新
|
548次组卷
|
5卷引用:2015届海市松江区高三上学期期末考试理科数学试卷
2015届海市松江区高三上学期期末考试理科数学试卷2015届海市松江区高三上学期期末考试文科数学试卷上海市松江区2018-2019学年高二第二学期期末考试数学试题上海市七宝中学2019-2020学年高二下学期4月月考数学试题(已下线)重难点02数列求和的五种解题方法-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
2018高三·江苏·专题练习
解题方法
10 . 设
个不全相等的正数
,…,
依次围成一个圆圈.
(1)设
,且
,…,
是公差为
的等差数列,而
,…,
是公比为
的等比数列,数列
,…,
的前
项和
满足
,求数列
的通项公式;
(2)设
,若数列
,…,
每项是其左右相邻两数平方的等比中项,求
;
(3)在(2)的条件下,
,求符合条件的
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58ed86115082ef4eca8105a42c5a331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16a76f125bf8132a48d2e930ec20251.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36290bba771bdbfd1172973e7ef2ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffe3635b25158f4992ff437fa4b440c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7dd7b0af4d4585a71e0d91fb1727e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4ba336b289b517b0905447b477a9d3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061a693b52b6327820b9352ecae36f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d61a111ab981437a0f71e6b063d8185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d422b12bde5d8dfb6468075db5520d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74e44711a47c8d105a8c0301a5fb6cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d9221c5055166e99aaa7b000cc5cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58ed86115082ef4eca8105a42c5a331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
(3)在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f87f22c524a4686608c6fba794b9217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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