Question

help me!/若|ab-2|+(b-2)的平方=0,求(1/ab)+{1/[(a+1)(b+1)]}+{1/[(a+

Answer 1

若|ab-2|+(b-2)的平方=0,求(1/ab)+{1/[(a+1)(b+1)]}+{1/[(a+2)(b+2)]}+…+{1/[(a+2004)(b+2004)]}的值.

因绝对值和平方数大于等于0,所以：

ab-2=0

b-2=0

a=1

b=2

1/1*2+1/2*3+1/3*4+..+1/2005*2006

=1-1/2+1/2-1/3+1/3-1/4+...+1/2005-1/2006

=1-1/2006

=2005/2006