因为：1/(1*2)=1/2=1-1/21/(3*4)=1/12=1/3-1/4.1/x(x+1)=1/x-1/(x+1)所以,1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+……+1/[(x+1998)(x+1999)]=1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+1998)-1/(x+1999)=1/x-1/(x+199...=1/x-1/(x+1999) 这一步是什么意思。怎么有两个除号？因为1/x-1/(x+1)+1/(x+1)-1/(x+2)+....+1/(x+1998)-1/(x+1999)中间全部消掉了。你仔细看一下，只留下了最前一项：1/x；和最后一项：1/(x+1999)