已知|a-1|+|ab-2|=0求1\ab+1\(a +1)(b+1)+1\(a+2)(b+2）+.1\(a+2006)(b+2006)的值急.

已知|a-1|+|ab-2|=0求1\ab+1\(a +1)(b+1)+1\(a+2)(b+2）+.1\(a+2006)(b+2006)的值急.
已知|a-1|+|ab-2|=0求1\ab+1\(a +1)(b+1)+1\(a+2)(b+2）+.1\(a+2006)(b+2006)的值
急.

已知|a-1|+|ab-2|=0求1\ab+1\(a +1)(b+1)+1\(a+2)(b+2）+.1\(a+2006)(b+2006)的值急.
绝对值大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立.
所以两个都等于0
所以a-1=0,ab-2=0
a=1,b=2/a=2
所以原式=1/1*2+1/2*3+1/3*4+……+1/2007*2008
=1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008
=1-1/2008
=2007/2008

|a-1|+|ab-2|=0
a-1=0,ab-2=0
a=1,b=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…… +1/（a+2006)(b+2006)
=1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2007×2008)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2007-1/2008)
=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008
=1/1-1/2008
=2007/2008