Question

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)...1/(x+2007)(x+2008)

Answer 1

1/x(x+1)=1/x-1/(x+1)

故原式=1/x-1/(x+1)+1/(1+x)-1/(x+2)+...+1/(x+2007)-1/(x+2008)=1/x-1/(x+2008)

楼主给分的话就更好了