By √(a- 1)+(ab-2)？ =0 a= 1, ab=2 (because both formulas are numbers greater than or equal to 0 and add up to 0, it can only be 0).

So a = 1 and b = 2.

Substitution:1/2+1/(2 * 3)+1(3 * 4)+...+1/(2008 * 2009).

Note:1/(2 * 3) =1/2-1/3.

1/(3*4)= 1/3- 1/4

....

Therefore, the original formula =1/2+1/2-1/3+1/3-65438+4+...+1/2008-65438+

= 1- 1/2009=2008/2009