已知数列
.如果数列
满足
,
,其中
,则称
为
的“衍生数列”.
(Ⅰ)若数列
的“衍生数列”是
,求
;
(Ⅱ)若
为偶数,且
的“衍生数列”是
,证明:
的“衍生数列”是
;
(Ⅲ)若
为奇数,且
的“衍生数列”是
,
的“衍生数列”是
,….依次将数列
,
,
,…的第
项取出,构成数列
.证明:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d620a71a9448d3a5be7fd8d5fea7094e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad083576ed8ff766b6d7c2a59a1c448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7e6327ecd86c682863f4a89e619fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da65bfc5919df189631c53048808e4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7304f4a3860fb2ce6535b51166d21446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(Ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232a4957e93a83aa5f3dd7215b9be594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5be81852e6ae92135ad336a919e601c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0016748ebec31c2f1bd490cb53994536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ab198a23f10c51c5796772e9147305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefcd32ac3e94ba73126ab1c29f0dda2.png)
12-13高三上·北京西城·期末 查看更多[3]
更新时间:2016-12-01 13:49:09
|
【知识点】 数列的综合应用
相似题推荐
解答题-问答题
|
困难
(0.15)
【推荐1】数列
是正整数
的任一排列,且同时满足以下两个条件:
;②当
时,
(
).记这样的数列个数为
.
(Ⅰ)写出
的值;
(Ⅱ)证明
不能被4整除.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987e30395d91964ebd0395faf2f66600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8f93c54dad6360a159db2d17609ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd7b6f92256833e6b9b849db8d4cca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
(Ⅰ)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e565b629c1cde32e9b627ef6b954d4.png)
(Ⅱ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338326674cfb0887c21997a738905132.png)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
【推荐2】已知数列
的首项
,前
项和为
,且
.
(Ⅰ)求数列
的通项公式;
(Ⅱ)设函数
,
是函数
的导函数,令
,求数列
的通项公式,并研究其单调性.
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/d1bf94011c6f4dc8955009f0af2a7d61.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/9f9a4e686acb47a587716bbabecf9d8b.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/417be8dd3210495db61e6e565f901527.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/19e8748d2af8436584a764efbc7fbc08.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/dee44107a14241a6baec0d256f2a18ce.png)
(Ⅰ)求数列
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/d1bf94011c6f4dc8955009f0af2a7d61.png)
(Ⅱ)设函数
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/ffccc57eb31e4a86a235adb171531306.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/956222234e094b4db64c9445a3b5c715.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/f4a3422c41c4452d9d105742816af790.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/5204ca68af544e14b180fb5d971e20d5.png)
![](https://img.xkw.com/dksih/QBM/2016/1/25/1572465804402688/1572465810554880/STEM/5de323f42bec4edbb29f39d577649559.png)
您最近一年使用:0次