Question

若|a-1|+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(

Answer 1

根据题意得

a-1=0 ab-2=0

解得

a=1 b=2

于是

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+……+1/(a+2005)(b+2005)

=1/1x2+1/2x3+1/3x4+...+1/2006x2007

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2006-1/2007)

=1-1/2+1/2-1/3+1/3-1/4+...+1/2006-1/2007

=1-1/2007

=2006/2007