1 . 由
,
,
,
,
,
,
,
,
,
按任意顺序组成的没有重复数字的数组,记为
,设
,其中
.
(1)若
,求
的值;
(2)求证:
;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d41baa5854760c61b58e4813c0dc23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3b9d0ea6fb9bfc3f298783bb156934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a926a5378a8dc9f9097eeb8ad3ac1d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202957f2a77c9db7845629c5a4cd8c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3293f12a66981b2d973b5ea27c319ed6.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e873ae3fcc2ceb24991d525073b7e8b.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3293f12a66981b2d973b5ea27c319ed6.png)
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名校
2 . 给定一个n项的实数数列
,任意选取一个实数c,变换
将数列
变换为数列![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5280b3866264f8c266fbcfc3de96fe.png)
,再将得到的数列继续施行这样的变换,这样的变换可以连续施行多次,并且每次所选择的实数c可以不相同,将第
次变换记为
,其中
为第
次变换时选择的实数.如果通过k次变换后,数列中的各项均为0,则称
为“
次归零变换”,如
项数列
有“
次归零变换”
.
(1)对数列
,请给出其一个“
次归零变换”,其中
;
(2)求证:对任意
项数列,都存在“
次归零变换”;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53032c9a9a3edca24a7ed909e29a58b.png)
(3)分别判断两个数列
与![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b09a30c1f614670c58260ac05637fa6.png)
是否存在“
次归零变换”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71440f7f7adb82343de4e1fe714844c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e5927e6b179a7df32697f18ba04b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5280b3866264f8c266fbcfc3de96fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd261890430da46de995859443c31a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0c165709cb397edbdf03aecee92bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5925987d5a6eb1ce1fec68b810cb6fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb41001678e62a7f251aca18ba87223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392131fb1129db593075a41e42614c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1925f666f670a98809ce07b2db292642.png)
(1)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63541441d26f277d9ed7816c089c6b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32122984badd2651714490544ab42682.png)
(2)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc321599521a98661ed719cc82ca87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53032c9a9a3edca24a7ed909e29a58b.png)
(3)分别判断两个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f28c61ca6fda7a77fdae8b39b41519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b09a30c1f614670c58260ac05637fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4259bd8918d091c52eb0bd5e3e0805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3493454f81c555d65d46357d719c5fdf.png)
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