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815

Part of 2012 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 815

Source: 196? Nara Medical College entrance exam

5/16/2012
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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