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
解题方法
2 . 已知直角梯形
,
,
,
,扇形圆心角
,
,如图,将
,
以及扇形
的面积分别记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
的表达式,并指出其大小关系(不需证明);
(2)用
表示梯形
的面积
;并证明:
;
(3)设
,
,试用代数计算比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36572a10fcb483a9abb63a5039e09ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201339005285d682fbc2cf65fbabddd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36477401af8ec19b82d682ab184753a2.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fec41d46ca97d3e900ef1db5a1f002c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be31dfad4f16cf1f2158b3011e3b68b9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e8d7d33749979b7d7acc17532d86b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7787a01998f68ccc931c00ccb475f6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bf4af3d4543cada4b52871ac9dfb1a.png)
您最近一年使用:0次
2023-07-09更新
|
598次组卷
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