Question

已知ab-2的绝对值与b-1的绝对值互为相反数 1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1

Answer 1

因为：ab-2的绝对值与b-1的绝对值互为相反数

所以：ab-2=0

b-1=0

则：a=2,b=1

代入原式化简得

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2006)(b+2006)

=1/2+1/(2+1)(1+1)+1/(2+2)(1+2)+...+1(2+2006)(1+2006)

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)

=1-1/2008

=2007/2008