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sec(2π2015)+sec(4π2015)+sec(6π2015)+…+sec(2014π2015)= ?\large{\sec \left( \dfrac{2\pi}{2015} \right) + \sec \left( \dfrac{4\pi}{2015} \right) + \sec\left( \dfrac{6\pi}{2015} \right) + \ldots + \sec \left( \dfrac{2014\pi}{2015} \right) = \ ? }sec(20152π)+sec(20154π)+sec(20156π)+…+sec(20152014π)= ?
Bonus : Generalize the sum ∑k=1nsec(2kπ2n+1)\displaystyle \sum_{k=1}^n \sec \left( \dfrac{2k\pi}{2n+1} \right) k=1∑nsec(2n+12kπ) in terms of nnn with a proper derivation without using methods like Induction.
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