一道算术题的简便算法

题目

一道算术题的简便算法
1+1/6+1/12+1/20+1/30+1/42+1/56 = 多少俄 .

答案

1+1/6+1/12+1/20+1/30+1/42+1/56 =1+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8) =1+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8 =1+1/2-1/8 =1又3/8