名校
1 . 已知等比数列
的首项
,数列
前
项和记为
,前
项积记为
.
(1) 若
,求等比数列
的公比
;
(2) 在(1)的条件下,判断
与
的大小;并求
为何值时,
取得最大值;
(3) 在(1)的条件下,证明:若数列
中的任意相邻三项按从小到大排列,则总可以使其成等差数列;若所有这些等差数列的公差按从小到大的顺序依次记为
,则数列
为等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e03cef5974ebfe9072f704c76f7f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1) 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafa9c1774dfbd599d5871ae4efb585c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2) 在(1)的条件下,判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c991692d281ea8c2fda692113809f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f99eb2934ccfb01ea9041053350190f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3) 在(1)的条件下,证明:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde658ec4dd02510bde861c33d7d60a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
您最近一年使用:0次
名校
2 . 若
,则
,
,
的大小顺序是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64839dc7ca709f6546399dcb84141b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e225a138f6611d48a8582e2f561ec048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883e58ed061e7d1dfd98d05408ac156a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22cbe3b3f024664dcd8c02b25c6a24c8.png)
您最近一年使用:0次