|a-1|+|b-2|=0绝对值大于等于0,相加为0则都等于0所以a-1=0,b-2=0a=1,b=2所以1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)=1/1*2+1/2*3+1/3*4+.+1/2010*2011=1-1/2+1/2-1/3+1/3-1/4+.+1/2010-1/2011=1-1/201...