1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.1/(x+99)(x+100) =1/x-1/x+1+1/(x+1)-1/(x+2)+1/(x+2)-1/(1+3)+.+1/(x+99)-1/(x+100) =1/x-1/(x+100)