名校
解题方法
1 . 根据统计数据,某种植物感染病毒之后,其存活日数X满足:对于任意的
,
的样本在
的样本里的数量占比与
的样本在全体样本中的数量占比相同,均等于
,即
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4111fbeeb20975034f051295bc7bb1f2.png)
__________ ,设
,
的前n项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05d83daef7bb72f157ed504d3a1708c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bbadf6bea687b3de5dd1afe160a020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ce9db5574a2df6184bdc7cd13b208a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc7e207019873e3b048a13d4876c952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4111fbeeb20975034f051295bc7bb1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea3df8f05aab080084fe846c692c321.png)
![](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/04c2864e2ec3416cc4c081ac1f71a0af.png)
您最近一年使用:0次
2024-06-09更新
|
543次组卷
|
3卷引用:辽宁省大连市第二十三中学2024届高三下学期校模拟考试数学试题
名校
解题方法
2 . 设等比数列
的前
项和为
,已知
.
(1)求数列
的通项公式.
(2)求数列
的前
项和
.
![](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/142eb0a5da189e1c6c532ebf9ae52b94.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2024-04-18更新
|
1929次组卷
|
5卷引用:辽宁省大连市二十四中学2023-2024学年下学期高三第五次模拟考试数学卷数学
3 . 已知数列
是正项等比数列,
是等差数列,且
,
,
,
(1)求数列
和
的通项公式;
(2)
表示不超过x的最大整数,
表示数列
的前
项和,集合
共有4个元素,求
范围;
(3)
,求数列
的前
项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5c206e70fdd64f4a3271fa68e5b2ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c519b98e1955f805ad21af88991e0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471584358a4c23a08378b2d8fa02c8c4.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ef48976a52cc4a2be7c46a98426c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10588e175c133b5387712aae98af243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b17a9b9bb8bf6bb9865e37f204da5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a0184899670c267c9abfd4654c73de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2595fc71a5a8cff69018fe66e3e9fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
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4 . 已知数列
的前n项和为
,
,且
.
(1)证明:数列
为等比数列,并求其通项公式;
(2)若______,求数列
的前n项和
.
从①
;②
;③
,这三个条件中任选一个补充在上面的横线上并解答问题.
注:如果选择多个条件分别解答,按第一个解答计分.
![](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/2e4424ac7dd09b764226ab6ff9e36564.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若______,求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0f044dc82a12fd1c71872f2ac12d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5b5451f8f8bd987d61b67cb29ef676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dece09ce17894e8c4c1b2fa03ba26496.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
5 . 已知各项均为正数的数列
,
满足:
,
,
.
(1)求数列
,
的通项公式;
(2)求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/335fac4f421788423059e5abd4fcdcab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c40361688108251c71bb8551cdf461.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec4bdc2a6d4fc387dc621f0b5a268c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-10-15更新
|
1639次组卷
|
4卷引用:辽宁省抚顺德才高级中学2023届高三硬核提分(八)数学试题
辽宁省抚顺德才高级中学2023届高三硬核提分(八)数学试题辽宁省沈阳市小三校2023-2024学年高三上学期10月联考数学试题(已下线)第05讲 4.3.2等比数列的前n项和公式(7类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)(已下线)第08讲 第四章 数列 重点题型章末总结-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第二册)
名校
解题方法
6 . 已知数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)设数列
满足
,求数列
的前
项和
.
![](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/350683edcadeed2ed72866506d8e2d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2464f1f6fdfa98d7f59cfdbded303025.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb78d3a4209ebbede94346ba8cfc997a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1fc4f23cc971972cf0b1033fe508b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
7 . 在数列
中,
,
.
(1)证明:数列
是等比数列;
(2)记数列
的前
项和为
,若关于
的不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b21f846c91c05d4c5e316a5d937b7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9308d36580e1ab11e343b660ec2d10.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac633587ba2da63197c35031722602db.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b66c56ce8a450614b456438f1fa2b2.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a0bfe7b7d022f7e1480d762f4cd246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-05-29更新
|
653次组卷
|
4卷引用:辽宁省大连育明高级中学2023-2024学年高三下学期二模数学试题
名校
解题方法
8 . 已知数列
是各项为正的等比数列,满足
,
.数列
的前n项和为
且满足
,
,对任意
恒成立.
(1)求
,
的通项公式;
(2)数列
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6065aaa8f3f103d1bc960da8318ce35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3376eed650c085fa93a477ada3c39c35.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/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa310e821752065f028727bea0b68c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b67af73f586837594ab0db4b89baed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ecd541b7f122fc6e141678b3db8dd13.png)
您最近一年使用:0次
2023-04-24更新
|
785次组卷
|
2卷引用:辽宁省部分学校2022-2023学年高三下学期第二次模拟考试数学试题
解题方法
9 .
为数列
的前n项和,已知
.
(1)证明:
;
(2)保持数列
中各项先后顺序不变,在
与
之间插入数列
的前k项,使它们和原数列的项构成一个新的数列:
,
,
,
,
,
,
,
,
,
,…,求这个新数列的前50项和.
![](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/5c3353d45cb2814af9b2cd4c7bef1f30.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d2c8d7beb11c4052aad6325120a1af8.png)
(2)保持数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62951b356373d5591e79e9d9317430de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32d77b3d3c3dc28c9b1e580776d496c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32d77b3d3c3dc28c9b1e580776d496c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef941b0d4287e1c9a120f37467e19a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32d77b3d3c3dc28c9b1e580776d496c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef941b0d4287e1c9a120f37467e19a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad379ea66b83d8784e7040a82c7a4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
您最近一年使用:0次
10 . 若正整数m,n只有1为公约数,则称m,n互素,欧拉函数
的函数值等于所有不超过正整数k,且与k互素的正整数的个数,例如:
,
,
,
.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a276d8673c9fc5532dd7e2a855835a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f273d0f53eb89345c48806352ebc0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8113f70737283a31ba1c5af62a8118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ad996a846b9d32a7f92458481dd0d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927395aa8591d85cd6c4549d19479ec4.png)
A.![]() | B.数列![]() |
C.![]() | D.数列![]() ![]() ![]() |
您最近一年使用:0次
2023-03-27更新
|
827次组卷
|
3卷引用:辽宁省大连市二十四中、育明、八中三校2023届高三下学期3月联考数学试题
辽宁省大连市二十四中、育明、八中三校2023届高三下学期3月联考数学试题辽宁省沈阳市第二中学2022-2023学年高二下学期4月月考数学试题(已下线)专题05 数列 第三讲 数列与不等关系(解密讲义)