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+2007)(b+2007)的值

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+2007)(b+2007)的值
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+2007)(b+2007)的值

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+2007)(b+2007)的值
|ab-2|与|b-1|互为相反数,且|ab-2|≥0,|b-1|≥0
则ab-2=0
b-1=0
解得a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2007)(b+2007)
=1/2+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

两个绝对值互为相反数，则它们都等于0
所以ab=2，b=1，得出：a=2
所以后面的算式简化为：1-1/2+1/2-1/3+1/3-1/4....+1/2008-1/2009=1-1/2009=2008/2009

|ab-2|与|b-1|互为相反数
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)
=1/1*2+1/2*3+...+1/2008*2009
=1-1/2+1/2-1/3+...+1/2008-1/2009
=1-1/2009
=2008/2009