计算-1/2-1/6-1/12-1/20-……1/42

问题描述:

计算-1/2-1/6-1/12-1/20-……1/42
这是儿子的能力提升题,我算出来了是-6/7.

-1/2-1/6-1/12-1/20-……1/42
=-1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-.-(1/6-1/7)
=-1/2-1/2+1/3-1/3+1/4-1/4+1/5-.-1/6+1/7
=-1/2-1/2+1/7
=-1+1/7
=-6/7