如图所示,由若干个点组成形如三角形的图形,每条边(包括两个端点)有
个点,每个图形总的点数记为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebce85ea9bc18815ef8887057030a63.png)
________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed52e5cd3461f78bfe5644bb25d2d5e.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6b5b2fce677852d6731b60fec94cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebce85ea9bc18815ef8887057030a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed52e5cd3461f78bfe5644bb25d2d5e.png)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716738643345408/2745470505099264/STEM/d8c10a8704994aac814be6350a39265b.png?resizew=375)
更新时间:2021-06-18 08:16:57
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【推荐1】数列
的前项n和为
,满足
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c88abd936125401c8d7e3bc21f4396.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780a1b00ea3a4fec3069509041c84511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2de0d8c6fac12323e039a74448db071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c88abd936125401c8d7e3bc21f4396.png)
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解题方法
【推荐2】已知数列
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131bdfb203bdd32c9cadbbe8df3da94b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ba388f908a4b64e3b91c604ef089f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deda945164283569437cda6976fe35ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131bdfb203bdd32c9cadbbe8df3da94b.png)
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【推荐1】中国古代十进位制的算筹记数法,在世界数学史上是一个伟大的创造.算筹记数的方法是:个位、百位、万位……的数按纵式的数码摆出;十位、千位、十万位……的数按横式的数码摆出. 1~9这9个数字的纵式与横式表示数码如下图所示:
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402335031967744/2402494237130752/STEM/78d61032adf84d919c36b752a32f9554.png?resizew=315)
如138可用算筹表示为
,则
的运算结果可用算筹表示为______ .
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402335031967744/2402494237130752/STEM/78d61032adf84d919c36b752a32f9554.png?resizew=315)
如138可用算筹表示为
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402335031967744/2402494237130752/STEM/d3c3338089734f16ac0d282190248a9d.png?resizew=25)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3c6c3995634f983bdc86c0e470e6da.png)
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【推荐2】如图1,线段
的长度为1,在线段
上取两点
,
,使得
,以
为一边,在线段
上方作一个正六边形,然后去掉线段
,得图2中的图形;对图2中的最上方线段
作同样的操作,得图3中的图形;以此类推,能够得到以下一系列图形记第
个图形(图1为第1个图形)中所有线段长的和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6eb2fcf76cd58f6573a059ab1ab48b4.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95e81fcd744d8ffb168275315b36bc8.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/38594aa6-f26f-42ff-a304-cd1a2c603414.png?resizew=332)
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