1 . 对于无穷数列
,若
,
,则称数列
是数列
的“收缩数列”,其中
分别表示
中的最大项和最小项,已知数列
的前n项和为
,数列
是数列
的“收缩数列”
(1)若
求数列
的前n项和;
(2)证明:数列
的“收缩数列”仍是
;
(3)若
,求所有满足该条件的数列
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641df1c74b500ec998622b756a173115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f72dcd6cb9ea1a0c32a16e4914668bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e97b763ff0478b1bd535810c596b3cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6be5a8d331f694e083d67675e03d2af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dfe50de35322cd725884838f004c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1cebb9ccd8e2046a99c1473df04cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
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2020-09-03更新
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4卷引用:天津市滨海新区塘沽第一中学2020-2021学年高三上学期第五次月考数学试题