1/6+1/24+1/60+1/120+1/210+1/336+1/112
=(1*1/6)+(1/4*1/6)+(1/6*1/10)+(1/6*1/20)+(1/6*1/35)+(1/6*1/56)+(1/2*1/56)
=1/6*(1+1/4+1/10+1/20+1/35)+1/56*(1/6+1/2)
=1/6*(140+35+14+7+4)/140+1/84
=1/6*10/7+1/84
=21/84
=1/4