0.5+(-(1/6))+(-(1/12))+(-(1/20))+(-(1/30))+(-(1/42))=(简便)

来源：百度知道编辑：UC知道时间：2024/05/26 13:18:20

(-(1/6))+(-(1/12))+(-(1/20))+(-(1/30))+(-(1/42))=
-（1/2-1/3+1/3-1/4+……1/6-1/7）=-0.5+1/7

过程为1/2-1/6-1/12-1/20-1/30-1/42=1/2-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/7=1/2-1/7=5/14，绝对正确。

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