请帮忙解下题已知|ab-2|与|b-1|互为相反数,试求代数式.1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2004)(b+2004)

Question

请帮忙解下题
已知|ab-2|与|b-1|互为相反数,试求代数式.
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2004)(b+2004)

Answer 1

已知|ab-2|与|b-1|互为相反数,
b-1=0 b=1
ab-2=0 a=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2004)(b+2004)
=1/1x2+1/2x3+1/3x4+……+1/2005x2006
=1-1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006
=1-1/2006
=2005/2006