10-11高三上·广东·期中
名校
1 . 设数列
的通项公式为
.数列
定义如下:对于正整数
是使得不等式
成立的所有
中的最小值.
(1)若
,
,求
;
(2)若
,
,求数列
的前
项和公式;
(3)是否存在
和
,使得
?如果存在,求
和
的取值范围;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e2294cf1ed89c6edfb0d4897ef8087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3a0edce7c30258f1d134ca2d08a64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4edad0dfcd1d7f4225d15c305d1587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cad0f23354aa754ade482d849557fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b331f0c2ad289ef8161b7e59264a75a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4998bb3fc2c3c9bd277611d86d71578b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c320a0619c63a5b650a1a94c0a5679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a908e102552ad10f2e528b817549378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
您最近一年使用:0次
2016-11-30更新
|
1297次组卷
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6卷引用:上海市实验学校2018届高三上学期第三次月考数学试题
2 . 已知数列
满足
.
(1)求数列
的通项公式;
(2)对任意给定的
,是否存在
(
)使
成等差数列?若存
在,用
分别表示
和
(只要写出一组);若不存在,请说明理由;
(3)证明:存在无穷多个三边成等比数列且互不相似的三角形,其边长为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb712dca9d8f147872e6754bafb6c0a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)对任意给定的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad52924df9291d5d191d18e09374ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf1c130cb225fc18415ebb502e1b488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a703c4b29e8c39df29e2c518efae236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b37e71b5a4cc8b8ea89e47dd12b4783.png)
在,用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(3)证明:存在无穷多个三边成等比数列且互不相似的三角形,其边长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5500ffabc0887e1bc7f4ef6ec56b5e5c.png)
您最近一年使用:0次