1 . 把正整数按一定的规则排成如图所示的三角形数表,设
(
)是位于这个三角形数表中从上往下数第
行,从左往右数第
个数,如
.若
,则
与
的和为__________ .
1
2 4
3 5 7
6 8 10 12
9 11 13 15 17
14 16 18 20 22 24
……
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0017117fab6f8e863c540552588e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43366cf92d2bbd350b6f2dcc9e14d712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2f9b53662f542a1c894c91b24a80cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
1
2 4
3 5 7
6 8 10 12
9 11 13 15 17
14 16 18 20 22 24
……
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2 . 已知在平面直角坐标系中有一个点列:
,
,…,
.若点
到点
的变化关系为
(
),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1326d7b4c0c3bf743a830b88c47d7565.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07208953e4ed5c5ff9713e829604f50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa166b0618cc34d18b9c36d2cf106ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af64997ae53eb6697e5c04ec368d5f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6311acf03e6423b0450374682cb14d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f24bf37465feef73be23136e60285b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6faadd8c3d0501ff206e6aa5a643051d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1326d7b4c0c3bf743a830b88c47d7565.png)
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3 . 整数m,n满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705d0cd198f423d1a7d6b9a7999c18ee.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24aa90aa2d2ad600a5fce8ea1a88dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705d0cd198f423d1a7d6b9a7999c18ee.png)
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4 . 若向量
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8e23423ba05ff0072a71738caa5d65.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9966321783e7f781767870ba5af2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8e23423ba05ff0072a71738caa5d65.png)
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5 . 函数
满足
,则常数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59d46d237d30bf862090469c98da9f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535fbd4834ea07cadae1dcc39bb83913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e9bb42376c12d7d21702ae8062b25a.png)
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解题方法
6 . 设数列
满足
,且
,则通项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c2dc3e8291037e6b180d67b137c37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f200a5483af0cfa8f56068585cba52d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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解题方法
7 . 不等式
的解集为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d78849519f99b4fcf6f5aaee30df7e.png)
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解题方法
8 . 定义在整数集上的函数
满足:
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aa7165f452c8e8a84dbcc183b65f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4138e3a956d50c217cdd4799ff1edd.png)
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9 . 已知向量
,向量
,则
的最小值是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2aa1670a597db4dcc5e481c9eb41dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4bc0c419f5e85ede099956c486cbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2168f5bd84030844be63c929211c68e.png)
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10 . 记不超过x的最大整数为
,若集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72ef9665654c618812d35f99535549d.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe65fd88f6f84c855b9f564d50eebc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72ef9665654c618812d35f99535549d.png)
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