1 . “
序列”在通信技术中有着重要应用,该序列中的数取值于
或1.设
是一个有限“
序列”,
表示把
中每个
都变为
,每个0都变为
,每个1都变为0,1,得到新的有序实数组.例如:
,则
.定义
,
,若
中1的个数记为
,则
的前10项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeedb00753e7cf6d2631244ce112019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c928060da9aa0d459ca27a9e26d656cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeedb00753e7cf6d2631244ce112019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60a47fe3db1924469eb3c03f9073bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c928060da9aa0d459ca27a9e26d656cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02d9f149c12ef612345a0617650215e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bada33e0bb409c2b7c75f84b61c0864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28dc832f1e9e421ac03f848ac22eb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32ccd28d1aaf22369edb601d07c76ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8e99a137748fac22a827de8dae1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fd6f1e91e0d10c3b2421b59020f90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
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解题方法
2 . 我们知道,二维空间(平面)向量可用二元有序数组
表示;三维空间向盘可用三元有序数组
表示.一般地,
维空间向量用
元有序数组
表示,其中
称为空间向量的第
个分量,
为这个分量的下标.对于
维空间向量
,定义集合
.记
的元素的个数为
(约定空集的元素个数为0).
(1)若空间向量
,求
及
;
(2)对于空间向量
.若
,求证:
,若
,则
;
(3)若空间向量
的坐标满足
,当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1acd1459dd96e861e6e04abccb2a3817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c2a29087dbd2e7635da13f7d288c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a3c6c6fe94124d76957d9a8c837701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4e5fb9e41d1310778b0dda692066dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afad70ea217c830631639e8508ad410b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0196cb738ee760339a9e15c8e6d9a41.png)
(1)若空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4517944d03f267b87ee1c184f463dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a0d7cdd1e3a38753d1290d9de9f9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc51f796615bfd474cee9d4d80e1eae.png)
(2)对于空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09611387d4de23004d388c9a8dde3438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daee8af73118698c77e022651f69ef22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
(3)若空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd074bea5f4eb8f60729b75e970afda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3894099d6bf29b73086842a48da10174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1653bed33a88140f16d494e8454f5225.png)
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3 . 已知正项数列
的前
项和为
,且
.
(1)求
和
的值,并求出数列
的通项公式;
(2)证明:
;
(3)设
,求
的值(其中
表示不超过
的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584293c94385d782623501c23fa5c4a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f967dc472d616ba9fc64ef067871e94.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef81f388c2c14a3582f10bfed8f0c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c975bb563c21b4d0817f086375e42c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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4 . 已知数列
满足:
,
,且
,则数列
前n项的和
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54705470b92ff0b31ff49586f689a8f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知数列
的前
项和为
,
,
,且
是
,
的等差中项,则使得
成立的最小的
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c752ebe8516e7d3327f3410473d9a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0863cf59114f905e9ad3debc5572792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e9ac58a1c9d1d6234116b6c6159ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19f39beb2ca207137f0816d87332197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39222f0687c9124bddb35544bcc7798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9977377c6fd4716b7b388db2ff1c04dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.8 | B.9 | C.10 | D.11 |
您最近一年使用:0次
2024-04-07更新
|
1684次组卷
|
2卷引用:湖北省华中师范大学第一附属中学、湖南省湖南师范大学附属中学等三校2024届高三下学期4月模拟考试(二模)数学试卷
6 . 已知数列
的前
项和为
,且
.
(1)求数列
的通项公式;
(2)若存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d87c84f22c0c8eccf0b62fc57d62500.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6c6098cd1d27cd8c8e387bc143d811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-04-05更新
|
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|
6卷引用:湖北省华中师范大学第一附属中学、湖南省湖南师范大学附属中学等三校2024届高三下学期4月模拟考试(二模)数学试卷
7 . 已知数列
,
,对任意正整数k,
,
,
成等差数列,公差为k,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acca5aa6b2285d897a65c289c1b54ba.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7b6ecfdff9d2b29ef64d2a6f3343f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39773a450e3c30c72ead226d84e54563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069c88b849f37a1597cb7e9cdcb1e755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acca5aa6b2285d897a65c289c1b54ba.png)
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23-24高三下·湖南·开学考试
8 . 若数列
满足
,
,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdf53108bee755f5aa9a34ea4d163e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2be148605b1b98bf183b7052eb5657e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77288bfa684c2a9ca00c75743232a0e3.png)
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9 . 定义:在数列
中,
,其中d为常数,则称数列
为“等比差”数列.已知“等比差”数列
中,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519b9371e75c16d4fdfcb0522de706e4.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/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced4e381e8c3336848b8c436dbc584f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0abb8e74a6689eac83450f89a7e974.png)
A.1763 | B.1935 | C.2125 | D.2303 |
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|
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5卷引用:湖南省长沙市第一中学2024届高考适应性演练(三)数学试题
湖南省长沙市第一中学2024届高考适应性演练(三)数学试题(已下线)专题5-2数列递推及通项应用-12024年新高考Ⅰ卷浙大优学靶向精准模拟数学试题(六)湖北省宜荆荆恩2024届高三9月起点联考数学试题(已下线)模块三 专题5 数列中复杂递推式问题(高三人教A)
10 . 已知正数数列
满足
,且
.(函数
求导
次可用
表示)
(1)求
的通项公式.
(2)求证:对任意的
,
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4793e0fdb84ddee68d7edc60f99b05b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2771c5f04582c545e0f9afc8a2cb9597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7a9d8d130ed4f980289b8f2e69b966.png)
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湖南省永州市第一中学2024届高三上学期第一次月考数学试题(已下线)重难点突破08 证明不等式问题(十三大题型)(已下线)专题10 数列不等式的放缩问题 (练习)广东省广州市华南师范大学附属中学2023届高三下学期5月月考数学试题