因为(a-1)²+|ab-2|=0
所以：a-1=0,a=1
ab-2=0,b=2
1/ab+1/[a+1][b+1]+1/[a+2][b+2]+……+1/[a+2007][b+2007]
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2008*2009)
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2008-1/2009
=1-1/2009
=2008/2009