1/2+1/6+1/12+1/20+1/30+1/40简便计算就是不知道为什么要1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

1/2+1/6+1/12+1/20+1/30+1/40简便计算
就是不知道为什么要1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

1/40错了,应该是1/42
原式=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=1-1/2+1/2+1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7