1/2+1/6+1/12+1/20+1/30+1/45+1/56 1/2+1/6+1/12+1/20+1/30+1/45+1/56..打错了，是1/42

1/2+1/6+1/12+1/20+1/30+1/45+1/56 1/2+1/6+1/12+1/20+1/30+1/45+1/56..打错了，是1/42
1/2+1/6+1/12+1/20+1/30+1/45+1/56
1/2+1/6+1/12+1/20+1/30+1/45+1/56
..打错了，是1/42

1/2+1/6+1/12+1/20+1/30+1/45+1/56 1/2+1/6+1/12+1/20+1/30+1/45+1/56..打错了，是1/42
你估计抄错题了,应该是1/42不是1/45
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/(1*2)+1(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)
=1-1/2+1/2-1/3+1/3-1/4+1/4-15+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

1、题目可能有错。1/45 应该是1/42就刚好。
2、1/2=1-1/2 1/6=1/2-1/3 1/12=1/3-1/4 1/30=1/5-1/6 ………………
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