名校
1 . 设非常数数列
满足
,
,其中常数
,
均为非零实数,且
.
(1)证明:数列
为等差数列的充要条件是
;
(2)已知
,
,
,
,求证:数列
与数列
中没有相同数值的项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d716659722cbc0132626ceab9b404e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3cd71690942ef82b8dc04580efc93a.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcebe948fb198d4fde0df1a1abe680bc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0733e8dfacbad67bdb7c26930acddaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234dd79e0081ba0ebd0f7cd4d7d5bef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6d8a8a57db1c2fc7f465d2cfd2aa78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81e4c91a371984fd3d13330c902b07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18bc279fef6843dddded8abfa0fbe63e.png)
您最近一年使用:0次
2021-06-08更新
|
791次组卷
|
6卷引用:江苏省南京师范大学《数学之友》2021届高三下学期二模数学试题
江苏省南京师范大学《数学之友》2021届高三下学期二模数学试题(已下线)卷09 高二上学期12月阶段测-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)(已下线)第17题 数列解答题的两大主题:通项与求和-2021年高考数学真题逐题揭秘与以例及类(新高考全国Ⅰ卷)(已下线)专题08 数列-备战2022年高考数学(文)母题题源解密(全国乙卷)(已下线)查补易混易错点04 数列-【查漏补缺】2022年高考数学三轮冲刺过关(新高考专用)江苏省苏州市吴江区震泽中学2022-2023学年高二10月月考数学试题
20-21高二上·全国·单元测试
解题方法
2 . 设集合W由满足下列两个条件的数列{an}构成:①
;②存在实数M,使an≤M(n为正整数)
(1)在只有5项的有限数列{an}、{bn}中,其中a1=1,a2=2,a3=3,a4=4,a5=5,b1=1,b2=4,b3=5,b4=4,b5=1,试判断数列{an}、{bn}是否为集合W中的元素;
(2)设{cn}是等差数列,sn是其前n项和,c3=4,s3=18,证明数列{sn}∈W,并写出M的取值范围;
(3)设数列{dn}∈W,对于满足条件的M的最小值M0,都有dn≠M0(n∈N*)求证:数列{dn}单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc75a9da38151496ca2adce84a977b96.png)
(1)在只有5项的有限数列{an}、{bn}中,其中a1=1,a2=2,a3=3,a4=4,a5=5,b1=1,b2=4,b3=5,b4=4,b5=1,试判断数列{an}、{bn}是否为集合W中的元素;
(2)设{cn}是等差数列,sn是其前n项和,c3=4,s3=18,证明数列{sn}∈W,并写出M的取值范围;
(3)设数列{dn}∈W,对于满足条件的M的最小值M0,都有dn≠M0(n∈N*)求证:数列{dn}单调递增.
您最近一年使用:0次
名校
3 . 在无穷数列
中,
,
是给定的正整数,
,
.
(1)若
,
,写出
,
,
的值;
(2)证明:存在
,当
时,数列
中的项呈周期变化;
(3)若
,
的最大公约数是
,证明数列
中必有无穷多项为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d04a8b7a7595251251b8e0b7e665e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5453ec6a9e8b96357c888ea863ddcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9cce535c2a1e74ca53ffda6a74f08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3ede255fecf6aba650c90309d62670.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfec53e7ec3a3ba1c82a5c41e87fd258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f83381978ab0c8f4714bab33c875dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164c49a0a9d3f6e67c9a59393d5b68a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90d3b3bbc187e571ebd740190200b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879f722d685a282c1ce2d0ad4f4e5cba.png)
(2)证明:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17e3e3e11d5dc0724cd60e81875da73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40aac3b8bed3f6e9b79a1f7c0ff6c830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d04a8b7a7595251251b8e0b7e665e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5453ec6a9e8b96357c888ea863ddcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15befbdad977723a86194979c675ee5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15befbdad977723a86194979c675ee5d.png)
您最近一年使用:0次
4 . 数列
满足:
或
.对任意
,都存在
,使得
,其中
且两两不相等.
(1)若
,写出下列三个数列中所有符合题目条件的数列的序号;
①
;②
;③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6682443f327ff60ddf3e91cbe7821d99.png)
(2)记
.若
,证明:
;
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32034ab9eaa06e450e27d87e999ea9e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad657749a0e222333076c72bf949970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdb0c5b7a3e183c714fad838d246d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639c7e5f1e7e7ee5d5ee2f30b155bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c4d0383577207858e39b4b19b0853e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454cc6ac47d35ebc2b34af6a8047a44e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5305ea58d22efe7136d404b1d44634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e44f2f5b6cab3a33e24de2502ac0c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6682443f327ff60ddf3e91cbe7821d99.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6559598727fb120a5cdbf4f15510615d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743b4f6fde34464397b010cb45eabb7d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662276a5012893d881e7d1d882b5ea4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2022-05-29更新
|
536次组卷
|
9卷引用:北京市第十三中学2022届高三上学期期中考试数学试题
5 . 已知正项数列
的前项积为
,且满足
.
(1)求证:数列
为等比数列;
(2)若
,求n的最小值.
![](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/455e3d1c1bfb0b326c0e320f98e66b4c.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e7f1421d306e84f98d00b7c8652647.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198f065fed9980714262cc8aae060bb5.png)
您最近一年使用:0次
2021-12-12更新
|
2559次组卷
|
7卷引用:江苏省无锡市2021-2022学年高三上学期期中数学试题
江苏省无锡市2021-2022学年高三上学期期中数学试题江苏省南京市田家炳高级中学2021-2022学年高三上学期期中数学试题(已下线)重难点01 数列-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)高二数学下学期期中精选50题(压轴版)2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)专题26 数列的通项公式-4(已下线)专题10 数列通项公式的求法 微点5 构造法安徽省合肥市龙翔高复学校2023-2024学年高三上学期9月月考数学试题
解题方法
6 . 已知数列
满足:
.
(1)求证:存在实数
,使得
;
(2)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f94297a84a8edbda26f1e408444e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b5f8d2dffc1f7242321273af9e1211.png)
(1)求证:存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4f920d9543b750a6655ae41b86594b.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f94297a84a8edbda26f1e408444e1.png)
您最近一年使用:0次
2022-01-23更新
|
387次组卷
|
2卷引用:山东省青岛市4区县2021-2022学年高三上学期期末考试数学试题
7 . 在数列
中,令
,若对任意正整数
,
总为数列
中的项,则称数列
是“前
项之积封闭数列”.已知数列
是首项为
,公比为
的等比数列.
(1)判断:当
,
时,数列
是否为“前
项之积封闭数列”;
(2)证明:当
或
时,数列
是“前
项之积封闭数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ed833d8a76dd313ba221fd38dfa490.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/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)判断:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f45f5bc7c648c0e8924b4fa7b1ad08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86249e312aa1413fae0e3aa986e96deb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-12-01更新
|
283次组卷
|
4卷引用:河南省信阳市2021-2022学年高二上学期期中考试数学(文)试题
河南省信阳市2021-2022学年高二上学期期中考试数学(文)试题河南省信阳市2021-2022学年高二上学期期中考试数学(理)试题(已下线)2020年高考江苏数学高考真题变式题21-25题(已下线)模块三 专题2 新定义专练【高二下人教B版】
21-22高三上·北京·期中
名校
解题方法
8 . 数列
满足:
或
对任意i,j,都存在s,t,使得
,其中
且两两不相等.
(1)若
时,写出下列三个数列中所有符合题目条件的数列序号;①
;②
;③
;
(2)记
,若
证明:
;
(3)若
,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e75e942e95a7a0b97d942f5443d1fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad657749a0e222333076c72bf949970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47308c0fff29949ed1fd6c6b5d69a9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c4d0383577207858e39b4b19b0853e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e773df13fb21901539facef835181a8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5305ea58d22efe7136d404b1d44634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e44f2f5b6cab3a33e24de2502ac0c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e0a77cbe1ba74715e7c30f357b932c.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36663c33a0236d40df9ffebb911ff90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743b4f6fde34464397b010cb45eabb7d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a5db4d5e02aa7bf2c58ffb61feee90.png)
您最近一年使用:0次
2021-11-27更新
|
875次组卷
|
5卷引用:北京市第四中学2022届高三上学期期中考试数学试题
(已下线)北京市第四中学2022届高三上学期期中考试数学试题(已下线)专题04 数列(数学思想与方法)-备战2022年高考数学二轮复习重难考点专项突破训练(全国通用)北京景山学校2022届高三适应性考试数学试题北京市顺义牛栏山第一中学2023-2024学年高三上学期期中考试数学试题(已下线)北京市第五十五中学2023-2024学年高二上学期期末模拟数学试题
名校
解题方法
9 . 设数列{an}和{bn}的项数均为m,则将数列{an}和{bn}的距离定义为
.
(1)给出数列1,3,5,6和数列2,3,10,7的距离;
(2)设A为满足递推关系an+1=
的所有数列{an}的集合,{bn}和{cn}为A中的两个元素,且项数均为m,若b1=2,c1=3,{bn}和{cn}的距离小于2016,求m的最大值;
(3)记S是所有7项数列{an|1≤n≤7,an=0或1}的集合,T
S,且T中任何两个元素的距离大于或等于3,证明:T中的元素个数小于或等于16.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94717ffac0bb1ee27488f3a92a4314d.png)
(1)给出数列1,3,5,6和数列2,3,10,7的距离;
(2)设A为满足递推关系an+1=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ac6a3d09cf3568551a1980dce396a0.png)
(3)记S是所有7项数列{an|1≤n≤7,an=0或1}的集合,T
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b980d8446f130dfc405c196109e73ea4.png)
您最近一年使用:0次
2021-10-22更新
|
639次组卷
|
4卷引用:北京理工附中2022届高三10月月考数学试题
名校
10 . 已知
是定义在
上的函数,满足:①对任意
,均有
;②对任意
,均有
,又数列
满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d1ff1ccdca84a1474a5c6dcafa681b.png)
.
(1)若函数
,求实数a的取值范围;
(2)函数
在
上单调递减,且
,若存在
,使得当
时,均有
,求
的最小值;
(3)求证:“函数
在
上单调递增”是“存在
,使得
”的充分非必要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdfed8d6862125dc1fecfce0322a750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168163183a3d4663be45755f44676191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/396a1e488ef539bb911acd5b07d130b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d1ff1ccdca84a1474a5c6dcafa681b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f2524b5f2ab805ae17d9662e383f9b.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8d53a860280eddacdbfa087cb3f331.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdfed8d6862125dc1fecfce0322a750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ff5f5621db0dd6d5edaef8948a924b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0608b46bc3944e09545473cdebcd54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591c10d6af25780ba5bfcd82f2cb366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4efdd9db012a4c6150c19aee82498e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
(3)求证:“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdfed8d6862125dc1fecfce0322a750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5215b10fe01e2c2052cb38a1706bede.png)
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