我觉得你的题目打错了
题目可能是
1/6+1/12+1/20+1/30+1/42
但都是用裂项法...
1)(没打错)
原式=1/6+1/12+1/20+1/30+1/40
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/40
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/40
中间很多项都抵消
So 原式=1/2-1/6+1/40=43/120
2)打错了
原式=1/6+1/12+1/20+1/30+1/42
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
中间很多项都抵消
So 原式=1/2-1/7=5/14