如果有理数a,b满足ab+2的绝对值加1-b的绝对值为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+1/3*4+1/4*5+...+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2009-1/2010
=1-1/2010
=2009/2010