已知丨ab+2丨+丨a+1丨=0 ,则代数式1/(a-1)（b+1)+1/(a-2)(b+2)+…+1/(a-2009)x(b+2009)

题目

已知丨ab+2丨+丨a+1丨=0 ,则代数式1/(a-1)（b+1)+1/(a-2)(b+2)+…+1/(a-2009)x(b+2009)

答案

丨ab+2丨+丨a+1丨=0
绝对值、都大于等于0
相加为0则各项均为0
那么ab+2=0
a+1=0
所以a=-1,b=2
所以1/(a-1)（b+1)+1/(a-2)(b+2)+…+1/(a-2009)x(b+2009)
=-(1/2*3+1/3*4+1/4*5+……+1/2010*2011)
=-(1/2-1/3+1/3-1/4+……+1/2010-1/2011)
=-(1/2-1/2011)
=-2009/4022