A Sharp Inequality for a Trigonometric Sum |
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| Authors: | Horst Alzer Stamatis Koumandos |
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| Institution: | 1. Morsbacher Str. 10, D-51545, Waldbr?l, Germany
2. Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus
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| Abstract: | We prove that the inequality $$-\frac{1}{2}\leq {\sum\limits_{k=1}^{n}} \left( \frac{{\rm cos}(2kx)}{2k - 1}+\frac{{\rm sin}((2k - 1)x)}{2k} \right)$$ holds for all natural numbers n and real numbers x with ${x \in 0, \pi]}$ . The sign of equality is valid if and only if n = 1 and x = π /2. |
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