|ab-2|与|b-1|互为相反数,|ab-2|+|b-1|=0
得ab-2=0,b-1=0 a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)
=1/1*2+1/2*3+.1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+.1/2009-1/2010
=1-1/2010
=2009/2010
|ab-2|与|b-1|互为相反数,|ab-2|+|b-1|=0
得ab-2=0,b-1=0 a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)
=1/1*2+1/2*3+.1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+.1/2009-1/2010
=1-1/2010
=2009/2010