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)
=9-(1/2+1/6+1/12+1/20……+1/90)
=9-[1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+……+(1/9-1/10)]
=9-[1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+(1/9-1/10)]
=9-(1-1/10)
=8+1/10
=8又1/10