求一道初中数学题！

绝对值岩伏陪都是非负数
两个非负数互为相反数,那粗蠢么这两个数都是0
ab-2=0
b-1=0
解得:b=1,a=2

1/ab+1/(a+1)(b+1)+1/(a=2)(b+2)+......+1/(a+2008)(b+2008)
=1/(1*2)+1/(2*3)+...+1/(2009*2010)
=1-1/2+1/厅野2-1/3+...+1/2009-1/2010
=1-1/2010
=2009/2010

|ab-2|=|b-1|=0 b=1 a=2
so 1/2+1/3*2+1/4*3+.....+1/冲埋戚液枣2010*2009
=1/散陵2+1/2-1/3+1/3-1/4+....+1/2009-1/2010
=1-1/2010=2009/2010

a=2,b=1

1/ab+1/蔽段(a+1)(b+1)+1/(a=2)(b+2)+......+1/(a+2008)(b+2008)
=1/(1*2)+1/团枝(2*3)+...+1/(2009*2010)
=1-1/2+1/2-1/3+...+1/2009-1/2010
=1-1/2010
=2009/宏或誉2010

b=1，a=2

|ab-2|与|b-1|都是非负数则胡，且互培伍为相孙中拦反数，所有|ab-2|与|b-1|都为0，解得b=1,a=2
然后................

由已知|ab-2|与|b-1|互为相郑前反数，有：ab=2，b=1 那消丛培么a=2
又有1/拿唯(n+1)(n+2)=1/(n+1)-1/(n+2)
那么，
1/(1*2)+1/(2*3)+...+1/(1+n)(2+n)=1-1/2+1/2-1/3+...+1/(1+n)-1/(2+n)=1-1/(2+n)=(n+1)/(n+2)
将n=2007,n=1999代入得

1 1 1 1
—+ ---------- + ---------- + ......+ ---------------- =2008/2009
ab (a+1)(b+1) (a+2)(b+2) (a+2007)(b+2007）

1 1 1 1
—+ ---------- + ---------- + ......+ ---------------- =2000/2001
ab (a+1)(b+1) (a+2)(b+2) (a+1999)(b+1999)