1/4+1/12+1/24+1/40+1/84+1/112+1/144+1/180
问题描述：
1/4+1/12+1/24+1/40+1/84+1/112+1/144+1/180
答
1/4+1/12+1/24+1/40+1/84+1/112+1/144+1/180
=1/4+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)+(1/12-1/14)+(1/14-1/16)+(1/16-1/18)+(1/18-1/20)
=1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/12-1/14+1/14-1/16+1/16-1/18+1/18-1/20
=(1/4+1/4)-(1/6-1/6)-(1/8-1/8)-(1/10-1/12)-(1/14-1/14)-(1/16-1/16)-(1/18-1/18)-1/20
=1/2-1/60-1/20
=13/30
如果在1/40后再加上1/60,计算时会更简便.