解：因为[a-1]+[ab-2]=0所以a=1，b=21/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2013)(b+2013)=1/2+1/(2*3)+1/(3*4)+……+1/(2014*2015)=1-1/2+1/2-1/3+1/3-1/4+……+1/2014-1/2015=1-1/2015=2014/2015
