Question

已知/ab－2/与／b－1／互为相反数,试求代数式1 1

Answer 1

|ab-2|=-|b-1|

|ab-2|+|b-1|=0

所以ab-2=b-1=0 得到a=2 b=1

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2004)(b+2004)

=1/2+1/2*3+1/3*4+...+1/2005*2006

=(1-1/2)+(1/2-1/3)+.+(1/2005-1/2006)

=1-1/2006

=2005/2006