WBJEE · Maths · Trigonometric Ratios & Identities
The sum of the series \(\sum_{n=1}^{\infty} \sin \left(\frac{n ! \pi}{720}\right)\) is
- A \(\sin \left(\frac{\pi}{180}\right)+\sin \left(\frac{\pi}{360}\right)+\sin \left(\frac{\pi}{540}\right)\)
- B \(\sin \left(\frac{\pi}{6}\right)+\sin \left(\frac{\pi}{30}\right)+\sin \left(\frac{\pi}{120}\right)+\sin \left(\frac{\pi}{360}\right)\)
- C \(\sin \left(\frac{\pi}{6}\right)+\sin \left(\frac{\pi}{30}\right)+\sin \left(\frac{\pi}{120}\right)\) \(+\sin \left(\frac{\pi}{360}\right)+\sin \left(\frac{\pi}{720}\right)\)
- D \(\sin \left(\frac{\pi}{180}\right)+\sin \left(\frac{\pi}{360}\right)\)
Answer & Solution
Correct Answer
(C) \(\sin \left(\frac{\pi}{6}\right)+\sin \left(\frac{\pi}{30}\right)+\sin \left(\frac{\pi}{120}\right)\) \(+\sin \left(\frac{\pi}{360}\right)+\sin \left(\frac{\pi}{720}\right)\)
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