因为a-1的绝对值与ab-2ab-2的绝对值都大于等于0,而a-1的绝对值+ab-2的绝对值=0,
所以a-1=0,ab-2=0,
解得a=1,b=2
1/ab+1/(a+1)(b+1) +.+1/（a+2005)(b+2005)
=1/1*2+1/2*3+1/3*4+……+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010