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1 . 若三角形三边成等比数列,则公比q的范围是_____ .
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2020-07-25更新
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629次组卷
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12卷引用:2003年北京市中学生数学竞赛_高一试题
2003年北京市中学生数学竞赛_高一试题北京五中2020届高三(4月份)高考数学模拟试题第一届高二试题(初赛)-“枫叶新希望杯”全国数学大赛真题解析(高中版)上海市上海中学2018-2019学年高一下学期期末数学试题上海市上海中学2018-2019学年高二下学期期末考试数学试题沪教版 高二年级第一学期 领航者 第七章 7.3 等比数列(1)沪教版(上海) 高二第一学期 新高考辅导与训练 第7章 数列与数学归纳法 阶段训练2(已下线)4.3.1 等比数列的性质2课时沪教版(2020) 选修第一册 领航者 第4章 4.2 第1课时 等比数列及其通项公式(1)(已下线)4.2等比数列及其通项公式(第1课时)(作业)(夯实基础+能力提升)-2022-2023学年高二数学精品教学课件(沪教版2020选择性必修第一册)沪教版(2020) 选修第一册 高效课堂 第四章 4.2 等比数列(1)(已下线)第03讲 等比数列及其前n项和(九大题型)(讲义)-3
2 . 已知数列
:
,其中
是方程
的两个根,
求证: (1)对任意正整数
,都有
;
(2)数列
中的项都是正整数,且任意相邻两项都互质.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74df23ef1c8916c62f9b23a59c567f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffdbc2dd999c9e421bdc1e516d99206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d425033162db73dac1ec662964b120.png)
求证: (1)对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502fa2b7493da2df086efda58bc09ac7.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
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3 . 如图,已知凸四边形
的对角线交于点
,
、
、
、
分别为
、
、
、
的内切圆圆心,且对应的内切圆半径
、
、
、
满足关系式
.
求证:(1)四边形
存在内切圆;
(2)
、
、
、
四点共圆.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dacb04fa29178c0af4353e4369a7e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c8942e253abf1f64b09fa7d83b9e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7ffcd1925a2b1259221c6a476152f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9a6eeeebf3cff569578d7366b755aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314c024e7e1467e8c1e0ccdb96007462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2cb48c0a69b8c420c0b64b2bfa1ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4804e9b295d3b8de7f05e9c4e8e30a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780f3b16573bc64d001506f4ede38bbd.png)
求证:(1)四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dacb04fa29178c0af4353e4369a7e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c8942e253abf1f64b09fa7d83b9e77.png)
您最近一年使用:0次
4 . 设
个质数
构成公差为
的等差数列,且
.求证
(1)当
是质数时,
;
(2)当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07db6ce04312bf94f979433d1caac1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0679d49843bad1b49d905662b4e37ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc707cbf72459c71ed9ed6efe4d9395.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e6766e4cfdcfb19daf5a0fedf5df17.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4437eb75ca2a5cb8d467802bd48933c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77969cd0bf8081594e9364e4fdc5ac3a.png)
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5 . 如图,正方形
内接于
,
为劣弧
上一点,
与
交于点
,
与
交于点
,记
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6568b070957fb3b1bd122620975ee792.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/9f43cda5-165b-4a9f-a40b-95da2198a401.png?resizew=140)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19692f3b7b3a02bf61abdafd5cb8c0e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b141b00b53e9f4f85f18ac40d6ccbc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6568b070957fb3b1bd122620975ee792.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/9f43cda5-165b-4a9f-a40b-95da2198a401.png?resizew=140)
A.1 | B.![]() | C.![]() | D.![]() |
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6 . 已知平面上九个点,任两点间的距离都不小于1.证明:其中至少存在两个点间的距离不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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7 . 方程
的所有根的立方和等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4c5df481627616043a37eaef9cbc46.png)
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8 . 如图, 动点 P 在以AB = 1为弦, 且含弓形角为
的弓形弧(含端点)上.设
, 试确定
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1313c6ef0f81bd8f033f63624b17d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38a21cd81fd401712ac1effae1c4a83.png)
![](https://img.xkw.com/dksih/QBM/2018/12/14/2096448314982400/2096840710062080/STEM/3634f4dd5d404b0e8f33b64ffa740e70.png?resizew=194)
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9 . 已知正整数
满足
,且
的最大值和最小值分别记作
和
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2ed87b1ce88cbcbf3177e7aa232a65.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c32ae1bfd9d3534675c1fb508fa3b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67cd35bc0c1e236d999da7eb5360126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2ed87b1ce88cbcbf3177e7aa232a65.png)
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10 . 已知
.则
被17除的余数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6802c6c55d4db229042310d783be43b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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