1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,⋯请根据上面算式中的规律,完成下面算式的运算.1/2+1/6+1/12+1/20+1/30+1/42+1/56

问题描述:

1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,⋯请根据上面算式中的规律,完成下面算式的运算.
1/2+1/6+1/12+1/20+1/30+1/42+1/56

(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8