a=1.ab=2.所以：b=2.1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)=1/1*2+1/(1+1)(2+1)+1/(1+2)(2+2)+.+1/(1+2009)(2+2009)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2010-1/2011)=1-1/2011=2010/2011