三年级的Marius没完没了地玩怎样产生三次方的整数,如痴如醉

打印 被阅读次数

Marius陶醉在他的数字世界里,几乎忘我。玩过了平方数,就捣鼓立方数。

所以今天我们就顺势聊他爱聊的三次方。

我说咱们是不是能写出每行第一项的表达式。我一时想不出。大约也就一两分钟后,Marius居然写出了 
kk + (k - 1)
kk - (k - 1)
这么有见地的表达式。不光是第一项,连最后一项也写出来了。这么快写出了带平方的表达式,我有点自叹不如了。

然后我们俩一起对一行求和,证明了和就是 S = kkk。Marius 开心坏了。下图中他删去了计算的中间步骤,因为都消掉了。

这时候他又扯出 X^4,说什么这个容易,因为 X^4 = (X^2)^2,而我们已经知道了X^2的规律了......

而妈妈还是只有羡慕的份 :D

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