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