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MathNet 2022-part-04 — 197 problems (EN–VI) Question 132

Math Olympiad Vault · MathNet 2022-part-04 — 197 problems (EN–VI)

Question 132

Let $f(x) = \frac{9^x}{9^x+3}$. Evaluate the sum
$$
\sum_{k=0}^{2021} f\left(\frac{k}{2021}\right).
$$