1 . 设
.在
的方格表的每个小方格中填入区间
中的一个实数.设第
行的总和为
,第
列的总和为
,
.求
的最大值(答案用含
的式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f98da45d4de19a962cfa1d186e2755a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ace7d64e7ff100db25a07330654d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af908bca1b10f5de7e2d8979989c806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aba126d3f244b529547fa33b1dc5f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a71c7129333f890292aa75bc1d080a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 设
为正整数,如果表达式
同时满足下列性质,则称之为“交错和”.①
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a717d685be4e0d53456f42e3cd401b.png)
;②
;③当
时,
(
);④规定:当
时,
也是“交错和”.
(1)请将7和10表示为“交错和”;
(2)若正整数
可以表示为“交错和”
,求证:
;
(3)对于任意正整数
,判断
一共有几种“交错和”的表示方法,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978be3cef71aa05b6ca98efb795dc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d70259b8ecc56afb8b3b15cf46082e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a717d685be4e0d53456f42e3cd401b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9b03740b24965e7196cbe91b82b252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e55143c8153a818863a3e5cf3cc6075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4cf5a951eef42eb9dff075e71210f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43649a490b881e3f7a5b6b7bee1a8b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59295942629ce535281d5066f14a65de.png)
(1)请将7和10表示为“交错和”;
(2)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978be3cef71aa05b6ca98efb795dc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7306bacb80799eeabd3fd46cb8632598.png)
(3)对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
3 . 若正整数
的二进制表示是
,这里
(
),称有穷数列1,
,
,
,
为
的生成数列,设
是一个给定的实数,称
为
的生成数.
(1)求
的生成数列的项数;
(2)求由
的生成数列
,
,
,
的前
项的和
(用
、
表示);
(3)若实数
满足
,证明:存在无穷多个正整数
,使得不存在正整数
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a573743c22f1988094a801651af5611e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1065440ee09654f97b50b5ef6a963ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef7fb812f8cb384ae86e75fb949ac66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30de4943aa77db7dc0b92b29b2aa93f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208400bfcdb85a19359c14f2c66e17c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fde3541708c770e48a06c28f9a3434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf09398436b9b00458c5d9b245ba287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c15a081508b98e5c53ebedc4be56c45.png)
(2)求由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b51c3c1cbed76bbb68d50f7df7209a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45c1e00ea3205d39449f3f9d64ec126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa7f3694402a60c3b50e39a76d87c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a28b156b7cb863056fda24d66fff68.png)
您最近一年使用:0次
真题
名校
4 . 若无穷数列
满足:只要
,必有
,则称
具有性质
.
(1)若
具有性质
,且
,
,求
;
(2)若无穷数列
是等差数列,无穷数列
是公比为正数的等比数列,
,
,
判断
是否具有性质
,并说明理由;
(3)设
是无穷数列,已知
.求证:“对任意
都具有性质
”的充要条件为“
是常数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e7146186b3a33ea5cbff137f9e3437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c0b488096f27c73fc960e27f3b864a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bc889cb3a977841028e444d62a4d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e690b25af1cd3e04b784a9f26be3e90e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)若无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c522c1c881528ab6f9708f6bdd4c4db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e52d55280e664b707f4e9ef4cb1554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928be44c53a39c116c715ab72f2f2d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb2db37e079b735acc41ea3035139e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8df5703574ef08007f1eea3cea18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4611e6b3af6a0f44f9d7a481f0e50d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89d1f32c1605cfdb8e8855051b9f6ec.png)
您最近一年使用:0次
2016-12-04更新
|
982次组卷
|
16卷引用:专题21 数列解答题(理科)-2
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