楼主
可以这样解
(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)对这个分析,(1/2+1/3+1/4+1/5)这个是相同的所以可以把这个提出来.(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)
=(1/2+1/3+1/4+1/5)*[(1+1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4)]
=(1+1/2+1/3+1/4+1/5)*1/5
=1/5+1/10+1/15+1
=41/30