Wacky Exponents!

Algebra Level 4

n=119999n/20009n/2000+3\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 ab\dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.


Source: Canadian Mathematics Olympiad 1.
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