巧算:1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
问题描述:
巧算:1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
答
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)
=1-1/9
=8/9