一直|a-1|与|b-3|互为相反数,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)的值

|a-1|与|b-3|互为相反数,a-1=0 a=1b-3=0 b=31/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)=1/1x3+1/2x4+1/3x5+……+1/2012x2004=(1-1/3+1/2-1/4+1/3-1/5+……+1/2012-1/2014）÷2=（1+1/2-1/2013-1/2014）...