名校
解题方法
1 . 已知数列
,其前
项和为
.
①数列
是等差数列,
②
(其中常数
),
③
三点共线,
④数列
是等比数列.
从四个命题中选一个命题作为条件,另一个命题作为结论制作一个正确命题,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c36e6a88dfa1c2265053d1a0bb9dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae879f815360b10de27112fc255a186b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f29b5a2a0855ebe60efe2657d0cf4e0.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65da4dc1bbf2fd72f36b5fea5ab89aaf.png)
④数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd015442628054692b8cc0a19c77d2bf.png)
从四个命题中选一个命题作为条件,另一个命题作为结论制作一个正确命题,并证明.
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名校
2 . 已知等差数列
的前
项和为
,集合
,集合B={![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50fffa7d0094903de0e00f3163f5de1.png)
x2﹣y2=1,x,y∈R},请判断下列三个命题的真假.若为真,请给予证明;若为假,请举出反例.
(1)以集合
中的元素为坐标的点均在同一条直线上;
(2)A∩B至多有一个元素;
(3)当a1≠0时,一定有A∩B≠∅..
![](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/06569415c90bddcefc033ca271bc4861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50fffa7d0094903de0e00f3163f5de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(1)以集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)A∩B至多有一个元素;
(3)当a1≠0时,一定有A∩B≠∅..
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