如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求：ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求:ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.(a+2003)(b+2003)/1 的值.注：

Question

如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求：ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.
如果有理数ab满足ab-2的绝对值+1-b的绝对值=0,试求:
ab/1 + (a+1)(b+1)/1 + (a+2)(b+2)/1 +.(a+2003)(b+2003)/1 的值.
注：

Answer 1

∵|ab-2|+|1-b|=0
∴ab-2=0,1-b=0
∴ab=2,b=1
∴a=2,b=1

1/ab + 1/(a+1)(b+1) + 1/(a+2)(b+2)+.1/(a+2003)(b+2003)
=1/1×2+1/3×2 +1/4×3+……..+1/2005×2004
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+……+(1/2004-1/2005)
=1-1/2+1/2- 1/3+ 1/3- 1/4+……+1/2004-1/2005
=1-1/2005
=2004/2005