1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
...
1/9900=1/99-1/100
1/3+1/12+1/20+1/30+……+1/9900=1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100
=2/3-1/100=197/300