有趣的数学【08】:很多时候,数学就是找规律

in #steempress5 years ago

现在,有很多人喜欢玩游戏,很大的一个原因在于:游戏能够给他们带来“征服”的快感。通过自己的努力(打游戏),享受逐步成功的感觉,有掌控感,也有成就感。他们不断地在游戏的过程中寻找规律,以期达到投入/产出比最高的结果。

很多父母都痛恨孩子打游戏,并想尽一切办法来阻止。实际上,换个角度来看,解数学题和打游戏的过程是差不多的,也是要发想法设法找规律求解,解题成功以后多巴胺分泌也很旺盛,能够让人感到极乐和狂喜。

如果父母想办法让孩子“陷入”解数学题这样的“游戏”,实际上也是解除游戏瘾的好方法。

那么,怎样才能让“陷阱”成功呢?

在我看来,多让孩子做一些“稀奇古怪”的数学题,前期让他们绞尽脑汁地想,后期再告诉他们简便方法,这会极大地引起他们的兴趣。

不过,要让他们不至于很快厌倦这种游戏,首先是必须掌握大量的公式,并多加练习形成条件反射。

怎么样才能这样呢?多看我写的文章就行啦~~

有趣的数学【07】:牢记公式,这是数学的倚天剑中,我们探讨了公式在数学中的重要地位。今天,我们再来看一下这把倚天剑的无敌魅力:
image

先说一下,今天的重点很简单,我们要记住的很简单,就是等差数列求和公式:
image


接下来,我们分析一下题面,找找规律,可以得出下面的关系(这一步非常关键,只有平时多练习才有可能联想到):
image

这么多等式,等号两边的项分别相加后,等式仍然成立。于是,就变成了这样:

原式 = 1+3+5+7+9+11+…………+…………

这样,原式的立方求和,就变成了一个奇数序列的求和。

那么,关键是要知道这个数列有多少个奇数。我们再分析一下上面的步骤,发现:
image
1的立方就是1个奇数相加;
2的立方就是2个奇数相加;
3的立方就是3个奇数相加;
4的立方就是4个奇数相加;
.
.
.
n的立方就是n个奇数相加;


所以,原式中,有
(1+2+3+4+5+6+7+8+……+n)个奇数相加。

根据等差公式,

1+2+3+4+5+6+7+8+……+n = (n/2)(1+n);


所以,共有 (n/2)(1+n)个奇数相加。
所以,
原式 = 1+3+5+7+9+11+…………+…………

根据等差数列公式,可得,n个奇数相加(1为首的奇数序列),和就是n的平方:
image

所以,原式等于 (n/2)(1+n)个奇数相加,答案为 (n/2)(1+n)的平方:
image

哈哈,做完这道题其实很有征服感,和打游戏差不多,不信你来试试!!

这就是数学的乐趣。

 

附上部分解题步骤:

image


Posted from my blog with SteemPress : https://kissfirer.000webhostapp.com/maths08

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我就是那個讀到

先说一下,今天的重点很简单,我们要记住的很简单,就是等差数列求和公式:

然後把書和筆丟下去玩兒的孩子了😂

Posted using Partiko Android

😂😂😂

Posted using Partiko iOS

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