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ASU 436 All Soviet Union MO 1986 |sin1|+|sin2|+|sin(3n-1)|+|sin(3n)|>8n/5.

Source:

August 7, 2019
trigonometryinequalities

Problem Statement

Prove that for every natural nn the following inequality is valid ∣sin⁡1∣+∣sin⁡2∣+∣sin⁡(3n−1)∣+∣sin⁡3n∣>8n5|\sin 1| + |\sin 2| + |\sin (3n-1)| + |\sin 3n| > \frac{8n}{5}
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