∵|a-2|+(b-1)²=0
∴a-2=0,b-1=0,
∴a=2 ,b=1
ab分之一+a+1*b+1分之一+...+(a+2007)*(b+2007)分之一
= 1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2008×2009)
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008+1/2008-1/2009
=1-1/2009
=2008/2009
∵|a-2|+(b-1)²=0
∴a-2=0,b-1=0,
∴a=2 ,b=1
ab分之一+a+1*b+1分之一+...+(a+2007)*(b+2007)分之一
= 1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2008×2009)
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008+1/2008-1/2009
=1-1/2009
=2008/2009