剪纸,又叫刻纸,是一种镂空艺术,是中国古老的民间艺术之一,已知某剪纸的裁剪工艺如下:取一张半径为2的圆形纸片,记为
,在
内作内接正方形,接着在该正方形内作内切圆,记为
,并裁剪去该正方形内多余的部分(如图所示阴影部分),记为一次裁剪操作,
重复上述裁剪操作
次,最终得到该剪纸.则第4次裁剪操作结束后所得
的面积为______ ;第n次操作后,所有裁剪操作中裁剪去除的面积之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4ce93705afe34d7c48d509885a155a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/4cf70112-e86b-44d0-ab3d-b744197477ac.png?resizew=116)
更新时间:2023-11-12 01:29:09
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相似题推荐
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较难
(0.4)
名校
【推荐1】侏罗纪蜘蛛网是一种非常有规律的蜘蛛网,如图是由无数个正方形环绕而成的,且每一个正方形的四个顶点都恰好在它的外边最近一个正方形四条边的三等分点上.设外围第一个正方形
的边长为1,往里第二个正方形为
,…,往里第
个正方形为
.那么第7个正方形的周长是____________ ,至少需要前____________ 个正方形的面积之和超过2.(参考数据:
,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
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【推荐2】数列
满足
,设
,则数列
的前
项和
的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b1c0296cca0d68f86f49dff0fb0337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb825f9831b2507778ec838c4d16ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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填空题-单空题
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解题方法
【推荐1】设集合
,对
的任意非空子集
,定义
为
中的最大元素,当
取遍
的所有非空子集时,对应的
的和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c9362c4222d95d02a04a958bfc1973.png)
______ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3772c9d3d64393c0fed39d8b3d1c1d5.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6cbc1242d9e0c3eca0d0835f450d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3292a7444b7e76515cee05ffe1eea50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3292a7444b7e76515cee05ffe1eea50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a1627192937fc5273a410f78dcc42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c9362c4222d95d02a04a958bfc1973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3772c9d3d64393c0fed39d8b3d1c1d5.png)
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【推荐2】已知数列
满足:
,定义:
表示整数
除以4的余数与整数
除以4的余数相同,例:
.设
,其中
,数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f37c41b3d37ebff1242f840b5fe0c0.png)
______ ;满足
的
最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bd1701942436577888033dddab56db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770e90a2561b0d1d2b29a3b79826ce3d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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