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.
by
Mark Mottian