1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90简便计算

1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/2*3+1/3*4+..+1/9*10
=(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1/2-1/10
=2/5

原式=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10=1/2-1/10=2/5

告诉你方法吧，1／6＝1/(2*3）＝1/2－1/3，把剩下的也化成这样就把中间的都消掉了，最后只剩一头一尾两个数了。

原式=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/2-1/10
=2/5

1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10=1/2-1/10=2/5