一道六年级分数简算题

题目

一道六年级分数简算题
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?
写出简算过程
再写出为什么

答案

=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)=(1-1/2)+(1/3-1/4)+(1/5-1/6)+...+(1/9-1/10)=1-1/10=9/10