巧算1-1/2+1/6+……

问题描述:

巧算1-1/2+1/6+……

1-1/2+1/6+1/12+1/20+……+1/72+1/90=1-1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/8-1/9)+(1/9-1/10)=1-1/10=9/10