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 \(a+b\).


Source: Canadian Mathematics Olympiad 1.
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