Question

已知|ab-2|与|b-1|互为相反数,试求代数式

Answer 1

|ab-2|与|b-1|互为相反数

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

|ab-2|,|b-1|都为非负数,两者和为0.两者必定都为0

ab-2=0,b-1=0

a=2,b=1

1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2007)(b+2007)

=1/2*1+1/3*2+1/4*3+.+1/2009*2008

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2008-1/2009)

=1-1/2009

=2008/2009