Question 130
Define $f(x) = \frac{a^{x}}{a^{x} + \sqrt{a}}$ for any $a \gt 0$. Evaluate
$$
\sum_{i=1}^{2012} f\left(\frac{i}{2013}\right).
$$
$$
\sum_{i=1}^{2012} f\left(\frac{i}{2013}\right).
$$
MathNet 2026 — Part 07 Question 130
Math Olympiad Vault · MathNet 2026 — Part 07