简便计算：1/6+1/12+1/20+1/30+1/42

简便计算：1/6+1/12+1/20+1/30+1/42
简便计算：1/6+1/12+1/20+1/30+1/42

简便计算：1/6+1/12+1/20+1/30+1/42
1/6+1/12+1/20+1/30+1/42
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=7/14-2/14
=5/14

1/6+1/12+1/20+1/30+1/42
=1/(2x3)+1/(3×4)+1/(5x6)+1/(6x7)
=(1/2-1/3)+(1/3-1/4)+(1/5-1/6)+(1/6-1/7)
=1/2-1/7
=5/14

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，左边相加1/6＋1/12＋1/20＋1/30＋1/42＝右边相加＝1/2－1/7＝5/14