Question 13
Prove that
$$
\sum_{k=0}^{n} (n + 1 - k) \sin((2k + 1)x) \geq 0, \quad \forall x \in [0, \pi].
$$
$$
\sum_{k=0}^{n} (n + 1 - k) \sin((2k + 1)x) \geq 0, \quad \forall x \in [0, \pi].
$$
MathNet 2026 — Part 06 Question 13
Math Olympiad Vault · MathNet 2026 — Part 06