1/3+1/8+1/15+1/24+1/35+...+1/80+1/99 怎么解

1/3+1/8+1/15+1/24+1/35+...+1/80+1/99
=1/2[(1-1/3)+(1/2-1/4)+...+(1/8-1/10)+(1/9-1/11)]
=1/2(1+1/2-1/10-1/11)
=36/55

1/3+1/8+1/15+1/24+1/35+...+1/80+1/99
=(1/2)*{[1-(1/3)]+[(1/2)-(1/4)]+[(1/3)-(1/5)]+...+[(1/7)-(1/9)]+[(1/8)-(1/10)]+[(1/9)-(1/11)]
=(1/2)*[1-(1/3)+(1/2)-(1/4)+(1/3)-(1/5)+...+(1/7)-(1/9)+(1/8)-(1/10)+(1/9)-(1/11)]
=(1/2)*[1+(1/2)-(1/10)-(1/11)]
=(1/2)*(72/55)
=36/55

一般项为1/[（n+1）^2-1]=1/n(n+2)=1/2[1/n-1/n+2]
1-1/3+1/2-1/4+1/3-1/5.。。。。1/98-1/100=3/2-1/99-1/100