对于
维向量
,若对任意
均有
或
,则称
为
维
向量. 对于两个
维
向量
定义
.
(1)若
, 求
的值;
(2)现有一个
维
向量序列:
若
且满足:
,求证:该序列中不存在
维
向量
.
(3) 现有一个
维
向量序列:
若
且满足:
,若存在正整数
使得
为
维
向量序列中的项,求出所有的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d5161d0f48af5d683e6437e7263a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475426b747f4fb1632ab89616983f44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca64ef9e0c3dd14e99d113dbbe973ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4988a9309359e790f4750d640a615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c267471981116d4f1efafbdb5d8a307a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5881e8018da8862a8d6ce6d8ad0961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
(2)现有一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e81fd1ebe96bd830c057f5f9c2c871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069e0779f6f4c055d2b1ae8819856aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164e87e68a2189679fd71b910611abf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deea0d65e8bba231c24029c419d8623e.png)
(3) 现有一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e81fd1ebe96bd830c057f5f9c2c871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea0a314158f7ddb302b29c03a7b4446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fb7a0db2d0ed0c3b60c989ec52da1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4d9051450515a74d33bbb0aa92be19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
2017·北京东城·二模 查看更多[5]
北京市东城区2017届高三二模理科数学试题北京市东城区2017届高三5月综合练习(二模)数学理试题北京市东城区2017届高三5月综合练习(二模)理数试题(已下线)卷02-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(北京专用)(已下线)北京市第四中学2023~2024学年高二上学期期中考试数学试题
更新时间:2017-05-04 17:39:15
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相似题推荐
解答题-问答题
|
较难
(0.4)
名校
【推荐1】已知数列
,从中选取第
项、第
项、
、第
项
,若
,则称新数列
为
的长度为m的递增子列.规定:数列
的任意一项都是
的长度为1的递增子列.
(Ⅰ)写出数列
的一个长度为4的递增子列;
(Ⅱ)设数列
.若数列
的长度为p的递增子列中,任意三项均不构成等差数列,求p的最大值;
(Ⅲ)设数列
为等比数列,公比为q,项数为
.判定数列
是否存在长度为3的递增子列:
?若存在,求出N的最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5f59bc23cf55f56312c9ed9806371f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af9e7b1c23db5584ad8521d4444d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc2b6b23da3e065820c15cf6c675e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608d034715f9b1dfb306f9c89d383582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e636879245230dd00a3ab3cbcfbfd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aeb1cbdad3d73306ca2ec905bfe961f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82079a5446d448fb1bea730b968d7e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅰ)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33339fa6f26d9c8a9459648af2485e3d.png)
(Ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f86c68104c0f89e3306b37265d6852a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅲ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec57bf360c18a9d0b3d8f89124b1257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a64e9c933af98e51cfeb0113961a88.png)
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【推荐2】阅读下列不等式的证法,再解决后面的问题. 证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c6453b90f28f864ef0b5ed664c9a81.png)
证:令
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07689c36e2f4a7ca93d98f40ce9c385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63750e1f59d21a9d913a1783c9e29e60.png)
,故
.
(1)若
,利用上述结论,证明:
;
(2)若
,模仿上述证法并结合(1)的证法,证明:
.(提示:若
,有
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c6453b90f28f864ef0b5ed664c9a81.png)
证:令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54ee01214753a0cd1de20e713771b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07689c36e2f4a7ca93d98f40ce9c385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63750e1f59d21a9d913a1783c9e29e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f09685d23264a068ba915f93d2d538a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c6453b90f28f864ef0b5ed664c9a81.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d8ef2ca213bdf42163dd6503ed8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c538d0141764bc692306b72b203e6ca1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ac0316a5700c2b6b2a007e5b469039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48c5178ba248de659f527fd08f0ec68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa70cba471ba57de69c962db483173f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964f30e8f81905c0c292ee34d6f272c8.png)
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解题方法
【推荐1】数列
:
满足
,称
为数列
的指数和.
(1)若
,求
所有可能的取值;
(2)求证:
的充分必要条件是
;
(3)若
,求
的所有可能取值之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a197918d989143a09028897f3a8a773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5e4185d2217f1ae68ad8f62586374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68424226b0d40c09b990f0eca3ff8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155c5f3a5c55e0c95191c5a893f63062.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0c2b029e1c1d7963c043ca041d82de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7bdaaf8b0adf10bf2ef6c1255b1dc.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047ec104459998bd3cbd339b29eaffc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00136ab4fd69ba9c28b47cd38442dc3a.png)
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解答题-证明题
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【推荐1】定义:有限非空数集
的所有元素的“乘积”称为数集
的“积数”,例如:集合
,其“积数”
.
(1)若有限数集
,求证:集合
的所有非空子集的“积数”之和
满足
;
(2)根据(1)的结论,对于有限非空数集
(
),记集合A的所有非空子集的“积数”之和
,试写出
的表达式,并利用“数学归纳法”给予证明;
(3)若有限集
,
①试求由
中所有奇数个元素构成的非空子集的“积数”之和
奇数;
②试求由
中所有偶数个元素构成的非空子集的“积数”之和
偶数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635cc4bb9a743b88c98fffad8ba1af00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5787e5d2863aa157213424a4803245.png)
(1)若有限数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d020cd453031ae9eede7961ec78f21a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319b6a5373bc8eb13772b8e6d047779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b64379aceaa2d008a48356937130c9e.png)
(2)根据(1)的结论,对于有限非空数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576ea0f23e66276d14e99a90c149c0dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)若有限集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994206101b7f04f92c5d4e2dcae7b8d.png)
①试求由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
②试求由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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【推荐2】已知2条直线将一个平面最多分成4部分,3条直线将一个平面最多分成7部分,4条直线将一个平面最多分成11部分,
;
条直线将一个平面最多分成
个部分(
)
(1)试猜想:
个平面最多将空间分成多少个部分(
)?
(2)试证明(1)中猜想的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de81010ee0b9b2ffec14092d830f02f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
(1)试猜想:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
(2)试证明(1)中猜想的结论.
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