解题方法
1 . 已知数列
的前n项和为
,若数列
满足:
①数列
为有穷数列;
②数列
为递增数列;
③
,
,
,使得
;
则称数列
具有“和性质”.
(1)已知
,求数列
的通项公式,并判断数列
是否具有“和性质”;(判断是否具有“和性质”时不必说明理由,直接给出结论)
(2)若首项为1的数列
具有“和性质”.
(ⅰ)比较
与
的大小关系,并说明理由;
(ⅱ)若数列
的末项为36,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2ebecf4a0f024b9fcf300196c52493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b0d89736a10c53998013df4a354396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633ae47f41318cce995ee5c6e5db4ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4a28346a8cfbf7fa850ef66ec18365.png)
则称数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d5fe6e813fbe15a3693fdbec7ac622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若首项为1的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(ⅰ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121b94d71ab1ccbbce1a3e53bc7d421a.png)
(ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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