1/2+1/6+1/12+1/25+1/30+1/42+1/52

1/2+1/6+1/12+1/25+1/30+1/42+1/52
1/2+1/6+1/12+1/25+1/30+1/42+1/52

1/2+1/6+1/12+1/25+1/30+1/42+1/52
1/2+1/6+1/12+1/25+1/30+1/42+1/52=
1/2+1/（2*3）+1/（3*4）+1/25+1/（5*6）+1/（6*7）+1/52=
1/2+1/2-1/3+1/3-1/4+1/25+1/5-1/6+1/52=
1-1/4+1/25+1/5-1/6+1/52=
3/4+6/25-1/6+1/52=
7/12+6/25+1/52=
9100/15600+3744/15600+300/15600=
（9100+3744+300）/15600=
13144/15600
楼上的都是错的...看清题没有?

最后个数应该是1/56？
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
1/56=1/7-1/8
原式=1-1/2+1/2-1/3+1/3...+1/6-1/7+1/7-1/8
=1-1/8=7/8

是1/2+1/6+1/12+1/20+1/30+1/42+1/56
=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
=1-1/8
=7/8