1 . 设集合
,其中
.
(1)写出集合
中的所有元素;
(2)设
,证明“
”的充要条件是“
”
(3)设集合
,设
,使得
,且
,试判断“
”是“
”的什么条件并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2745900c1c3372a3b37dfecc224d23e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576ea0f23e66276d14e99a90c149c0dc.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834919b3ab3c1c09a39f9c9840a9416c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f13b50acd120eb4c51efe6523c7b525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1c6fbf72f69e70f9d3fe3c8fa39fc1.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71de73e8625a91a3abb2bdc98f63cf60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfacc023f7aa57ab1f1421e68fafb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f06294bbd9e425f20a00dd606c923d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e185c096328c1d3b9dccd704261b3269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ed9b5d83428b4b7beb856825554703.png)
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2019-09-23更新
|
1035次组卷
|
2卷引用:上海市上海中学2018-2019学年高一下学期期末数学试题
名校
2 . 已知无穷数列
,
是公差分别为
、
的等差数列,记
(
),其中
表示不超过
的最大整数,即
.
(1)直接写出数列
,
的前4项,使得数列
的前4项为:2,3,4,5;
(2)若
,求数列
的前
项的和
;
(3)求证:数列
为等差数列的必要非充分条件是
.
![](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/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394d8b602b39602deee15b24181d1786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6812fe767ad55ac33946ca7ac80fa73e.png)
(1)直接写出数列
![](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/57ef6d44448092ebdb9e4a49d866a749.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6ec9a174e3792ce1a40310a21c378b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f41be870e84c819362787849770519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5e69a1736fce183c0227c991c14810.png)
(3)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c25b07fe756e6c37a703ca4a69fca8.png)
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