大数学家拉普拉斯曾经这样说过“数学本身赖以获得真理的重要手段就是归纳和类比”.事实上数学中的许多重要的定理和猜想都是通过归纳总结出来的,如欧拉公式:考查三棱锥、四棱锥、三棱柱、五棱柱等多面体,发现其顶点数
与面数
的和与棱数
相差
,即
,于是猜想任意凸多面体都具有这样的性质,后经过严格证明确实如此.利用上述思想,考查下列等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbb971b7fc7fa927160ec017b6f46dc.png)
则其中第
个等式左端和式最后一个数字、右端的结果分别是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a098e3851f80b3d3c273d34416c4778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbb971b7fc7fa927160ec017b6f46dc.png)
则其中第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
2019高三下·全国·专题练习 查看更多[2]
更新时间:2019-03-19 15:31:12
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【推荐1】对于大于1的自然数m,其三次幂可用奇数按一下方式进行“分裂”:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707d989b65a9b8e1b95f53e417170462.png)
对此,若
的“分裂数”中有一个是2017,则m=_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707d989b65a9b8e1b95f53e417170462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0c447cd416a669b45d23984b253e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36accab23dbd172687769aea43e5781c.png)
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【推荐2】如图是一个类似“杨辉三角”的图形,记
分别表示第
行的第
个数,第
个数,······第
个数,当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b2e35068487838f8f9fa3a90af5ed2.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7566f57586aef12c495395dc984a72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b974113b04534e6855489aebd8354d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b2e35068487838f8f9fa3a90af5ed2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/5968a381-ffe0-47b0-b25d-cdd55e240e58.png?resizew=176)
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