1/2+1/6+1/20+1/30+1/42+1/56+1/72=怎么算简便?

题目

1/2+1/6+1/20+1/30+1/42+1/56+1/72=怎么算简便?
没有1/90.

答案

用拆项法
1/2+1/6+1/20+1/30+1/42+1/56+1/72
=1/(1*2)+1/(2*3)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)
=1-1/2+1/2-1/3+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1-1/3+1/4-1/9
=7/12
不过照常规来说,应该有1/12这一项的,是不是少打了,反正方法是一样的,拆项相消.