1/2-1/3+1/4-1/5+1/6-1/7
=1/2+1/4+1/6-1/3-1/5-1/7
=1/2+1/4+1/6-[1/3+1/5+1/7]--2,4,6最小公倍数是12.3,5,7最小公倍数是105.
=6/12+3/12+2/12-[35/105+21/105+15/105]
=11/12-71/105--12*105=1260
=1155/1260-852/1260
=303/1260
=101/420
简便算法为:
1/2-1/3+1/4-1/5+1/6-1/7
=[3-2]/[2*3]+[5-4]/[5*4]+[7-6]/[7*6]
=1/6+1/20+1/42
=70/420+21/420+10/420
=[70+21+10]/420
=101/420