名校
1 . “解方程
”有如下思路:设
,则
在
上为减函数,且
,故原方程有唯一解
.类比上述解题思路,不等式
的解集为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc8fee13d6f190523ff6699e8fbc749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ffcaabba3c20311125062a56e64993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4ed4485745f1d259a3953c242b9cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a050b963ee0f077ba077d3e60c9f34a4.png)
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2020-04-16更新
|
910次组卷
|
3卷引用:河南省开封市兰考县等五县2018-2019学年高二下学期期中联考数学(理)试题
2 . 设
,
,
,将
的最小值记为
.则当
是偶数时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
__________ ;当
是奇数时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8ae469587300aece24a0599a630c2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ff741c0506b0619fe6c7b1990013af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7978d7bd6f6caf9ac9837ffce5f89654.png)
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3 . 杨辉三角,又称帕斯卡三角,是二项式系数在三角形中的一种几何排列.在我国南宋数学家杨辉所著的《详解九章算法》一书中用如图所示的三角形解释二项展开式的系数规律.现把杨辉三角中的数从上到下,从左到右依次排列,得数列:
.记作数列
,若数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e8149e93e8622a109580970db5abfd.png)
___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154febe3c6f31577c39ddc619450c6c2.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e8149e93e8622a109580970db5abfd.png)
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4 . 容器中有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
种粒子,若相同种类的两颗粒子发生碰撞,则变成一颗
粒子;不同种类的两颗粒子发生碰撞,会变成另外一种粒子. 例如,一颗
粒子和一颗
粒子发生碰撞则变成一颗
粒子.现有
粒子
颗,
粒子
颗,
粒子
颗,如果经过各种两两碰撞后,只剩
颗粒子. 给出下列结论:
① 最后一颗粒子可能是
粒子
② 最后一颗粒子一定是
粒子
③ 最后一颗粒子一定不是
粒子
④ 以上都不正确
其中正确结论的序号是________ .(写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
① 最后一颗粒子可能是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
② 最后一颗粒子一定是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③ 最后一颗粒子一定不是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
④ 以上都不正确
其中正确结论的序号是
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