√a- 1+(ab-2)^2=0

∴a= 1,b=2

∴ Original formula =1/(1* 2)+1(2 * 3)+1(3 * 4)+..+1/(2005 * 2000)

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

= 1- 1/2006

=2005/2006

If anyone plagiarizes my answer, I will kill you on behalf of the moon! )

P s: √ stands for root number; * stands for multiplication symbol; 2 represents the square.

thank you