1 . 已知数列
中,
,
,且数列中任意相邻两项具有2倍关系.记
所有可能取值的集合为
,其元素和为
.
(1)证明
为单元素集,并用列举法写出
,
;
(2)由(1)的结果,设
,归纳出
,
(只要求写出结果),并求
,指出
与
的倍数关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0515775e751e33b3df49f5ee93c6792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f80c39f8c5c95f9bcc70568a0d7bb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e406b775bbaa0ae52dab5b7bd384a6.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f762938f5c78eb72bafbb13bf85cba1.png)
(2)由(1)的结果,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d074c8ac48227c468fc562a34bfd93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f70131a0328c08bc3e917ca3dc7317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342d9276c99f962d3045ee8dab5a2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ddcaab517a37dcf7b2ba60db52d0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342d9276c99f962d3045ee8dab5a2d5.png)
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2021-02-05更新
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4卷引用:江西省宁冈中学2021-2022学年高一10月第一次段考数学(理)试题
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