MathDB

7

Part of 2017 Korea USCM

Problems(1)

Well-known trigonometric series bound

Source: 2017 South Korea USCM P7

8/15/2020
Prove the following inequality holds if {an}\{a_n\} is a deceasing sequence of positive reals, and 0<θ<π20<\theta<\frac{\pi}{2}. ∣∑n=12017ancos⁡nθ∣≤πa1θ\left|\sum_{n=1}^{2017} a_n \cos n\theta \right| \leq \frac{\pi a_1}{\theta}
seriesreal analysistrigonometric seriesinequalitiescollege conteststrigonometry