等差数列求和.1-5/6+7/12+9/20+11/30-13/42+15/56 请讲出缘由.

1-5/6+7/12+9/20+11/30-13/42+15/56
=1-(1/2+1/3)+(1/3+1/4)+(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)
=1-1/2-1/3+1/3+1/4+1/4+1/5+1/5+1/6-1/6-1/7+1/7+1/8
=1-1/2+1/4+1/4+1/5+1/5+1/8
=1-1/2+1/2+1/5+1/5+1/8
=1+1/5+1/5+1/8
=1+2/5+1/8
=40/40+16/40+5/40
=61/40