Wacky Exponents!

Algebra Level 4

$\large \displaystyle\sum_{n=1}^{1999}\dfrac{9^{n/2000}}{9^{n/2000}+3}$

If the value of the summation above can be expressed as $\dfrac ab$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .