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据说,德国数学家高斯八岁时,他的老师出了这样一道题:1+2+3+…+100=?他立即答出5050,老师感到很惊呀,问他用的是什么方法时,他说:“1和100,2和99,…每对和都是101,共50对,所以和为50×101=5050,他所用的方法就是配对法。高中《代数》第二册必修本44页推导等差列前n项和公式所使用的也是这种方法,这种方法不仅在中学数学中占有重要的地位,而且在近几年高考试卷中也常出现,下面就谈谈这种方法在中学数学解题中的应用。
It is said that when the German mathematician Gauss was eight years old, his teacher made such a question: 1+2+3+...+100=? He immediately answered 5050. The teacher was shocked and asked what method he used. He said: “1 and 100, 2 and 99, ... each pair is 101, a total of 50 pairs, so the sum is 50 x 101 = 5050, and the method he uses is the pairing method. High School ”Algebra" Volume 2 is compulsory This 44-page derivation of the first n terms and equations used in this formula is also a method of this kind. This method not only plays an important role in middle school mathematics, but also appears frequently in high test papers in recent years. Let’s talk about it here. The Application of Method in Middle School Mathematical Problem Solving.