a=1b=2则1/ab+1/（a+1)(b+1)+.....+1/(a+2004)(b+2004）的值

1/2+1/6+1/12+1/20+......+1/(2005*2006)

1/2=1-1/2

1/6=1/2-1/3

1/12=1/3-1/4

……

1/(2005*2006)=1/2005-1/2006

原式

=1-1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006

=1-(1/2-1/2)-(1/3-1/3)-(1/4-1/4)-……-(1/2005-1/2005)-1/2006

=1-0-0-0-……-0-1/2006

=2005/2006