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MathNet 1995 — Part 01 Question 25

Math Olympiad Vault · MathNet 1995 — Part 01

Question 25

Let $f(x) = \frac{9^{x}}{9^{x} + 3}$. Evaluate the sum
$$
f\left(\frac{1}{1996}\right) + f\left(\frac{2}{1996}\right) + f\left(\frac{3}{1996}\right) + \cdots + f\left(\frac{1995}{1996}\right)
$$