1/2+1/6+1/20+1/30+1/42+1/56+1/72
＝1/2+1/6+1/20+1/30+1/42+1/56+1/72+1/12-1/12
＝1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72-1/12
＝1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9-1/12
＝1-1/9-1/12
＝8/9-1/12
＝32/36-3/36
＝29/36
如果还有一个1/12的话
就是
1/2=1/（1*2）=1-1/2
1/6=1/（2*3）=1/2-1/3
1/12=1/（3*4）=1/3-1/4
1/20=1/（4*5）=1/4-1/5
1/30=1/（5*6）=1/5-1/6
1/42=1/（6*7）=1/6-1/7
1/56=1/（7*8）=1/7-1/8
1/72=1/（8*9）=1/8-1/9
原式=1-1/2+1/2-1/3+……+1/7-1/8+1/8-1/9=1-1/9=8/9