在《数理大地》第3、4期,周国镇老师给大家提出了一个趣味无穷的结论: 只要让a、b取一对一对的正整数,3a+2b/4a+3b像一个魔盒一样就会变成一个一个比2/3大比3/4小的分数. 并概括成:当n、a、b都是正整数时,n/n+1和n+1/n+2之间的分数是,即这里两端的分数n/n+1和n+1/n+2,每个分数的分子都比分母少1,较大分数的分子等于较小分数的分母. In the 3rd and 4th editions of “Mathematical Science”, Zhou Guozhen’s teacher put forward an interesting conclusion for everyone: Just let a and b take a pair of positive integers, 3a+2b/4a+3b like a box The same will become a score that is less than 2/3 larger than 3/4. And summed up: when n, a, b are all positive integers, between n/n+1 and n+1/n+2 The score is, that is, the scores n/n+1 and n+1/n+2 at both ends. The numerator of each score is less than 1 by the mother, and the numerator of the larger score is equal to the denominator of the smaller score.