因为Iab-2I与Ib-1I互为相反数,Iab-2I与Ib-1I都大于等于0,所以Iab-2I=Ib-1I=0,所以a=2,b=1
所以原式子为1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2011*2010)=1/1-1/2+1/2-1/3+1/3-1/4 +.+1/2010-1/2011=1-1/2011=2010/2011
注：1/2=1/1-1/2,1/(2*3)=1/2-1/3,1/(3*4)=1/3-1/4.