名校
解题方法
1 . 已知数列
满足对任意的
,均有
,且
,
,数列
为等差数列,且满足
,
.
(1)求
,
的通项公式;
(2)设集合
,记
为集合
中的元素个数.
①设
,求
的前
项和
;
②求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6cbbec0f900da8864d00e396893c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](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/5e506112c35bdf08b18460d233eb6595.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bc4ebb7c9c2323c75011db21226ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc96f796c19909fe80d0da1cd1d7823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b255b2aa8a99d13c0756a87906675c7f.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac6b8de4384ff605892e8de5263de13.png)
您最近一年使用:0次
2 . 已知数列
是首项为1的等差数列,数列
是公比不为1的等比数列,满足
,
,
.
(1)求
和
的通项公式;
(2)求数列
的前
项和
;
(3)若数列
满足
,
,记
.是否存在整数
,使得对任意的
都有
成立?若存在,求出
的值;若不存在,说明理由.
![](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/84672a737e1ba65228ffd2f0064a8c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40751e69baead4a0d5bea384aedfa6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dbe8fa82ab04f0a4ba4ad1c570c9aa1.png)
(1)求
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea6578afabc23f5d7041b88c3790dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614bac93e838d86d18422bed438368df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02b03f064cffd092bba6be3bfc95ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1505d56f0b35fe7f2de1fe1888036e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414847d018e36898bde4a88772c1d2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-11-30更新
|
1172次组卷
|
3卷引用:天津市南开中学2023-2024学年高三上学期第二次月考数学试卷
3 . 设
为正项数列
的前
项和,满足
.
(1)求
的通项公式;
(2)若不等式
对任意正整数
都成立,求实数
的取值范围;
(3)设
(其中
是自然对数的底数),求证:
.
![](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/8000fb7f840617503890d70eeccc7de6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b8b32b3ab01e12028a97d2da61f0b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9356db93ad4d580dd721f10e1ff9f13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1975bf0ac02835b5cca33dd7d496bc.png)
您最近一年使用:0次
2020-06-08更新
|
2026次组卷
|
6卷引用:天津市蓟州区第一中学2023-2024学年高三上学期第一次学情调研数学试题
天津市蓟州区第一中学2023-2024学年高三上学期第一次学情调研数学试题天津市第一中学2023-2024学年高三上学期开学考试数学试题浙江省温州市普通高中2018届高三下学期3月高考适应性测试数学试题(已下线)浙江省温州市2023届高三下学期3月高考适应性测试(二模)数学试题(已下线)专题10 数列通项公式的求法 微点10 数列通项公式的求法综合训练(已下线)专题07 数列-2