1/2+5/6+11/12+19/20+……+89/90
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+.+(1-1/90)
=1-1/2+1-1/6+1-1/12+1-1/20+.+1-1/90
=1-(1-1/2)+1-(1/2-1/3)+1-(1/3-1/4)+1-(1/4-1/5)+.+1-(1/9-1/10)
=1*8-1+1/2-1/2+1/3-1/3+1/4-1/4+1/5+.-1/9+1/10(因为从2开始到10结束,所以有8项)
=8-1+1/10
=71/10
=7又1/10