原式通分
1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
以此类推
原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+99)-1/(x+100)
=1/x-1/(x+100)