1/2+5/6+11/12+19/20+29/30+41/42=?
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)
=6-(1/2+1/6+1/12+1/20+1/30+1/42)
=6-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)
=6-(1-1/7)
=6-6/7
=5又1/7