解：1/2+1/6+1/12+1/20+1/30+1/42=9/12+5/60+1/42=10/12+1/42=5/6+1/42=36/42 =6/7
原式==1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=1-1/76/7
