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Today's calculation of Integral 815

Source: 196? Nara Medical College entrance exam

May 16, 2012
calculusintegrationtrigonometryfunctioncalculus computations

Problem Statement

Prove that : ∣∑i=0n(1−πsin⁡iπ4ncos⁡iπ4n)∣<1.\left|\sum_{i=0}^n \left(1-\pi \sin \frac{i\pi}{4n}\cos \frac{i\pi}{4n}\right)\right|<1.
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