The value of equals

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of lim⁡n→∞∑k=1nn−kn2cos⁡(4kn)\lim_{n\to\infty}\sum_{k=1}^{n}\frac{n-k}{n^2}\cos\left(\frac{4k}{n}\right) equals (1) 14sin⁡4+116cos⁡4−116\frac14\sin4+\frac1{16}\cos4-\frac1{16} (2) 14sin⁡4−116cos⁡4+116\frac14\sin4-\frac1{16}\cos4+\frac1{16} (3) 116(1−sin⁡4)\frac1{16}(1-\sin4) (4) 116(1−cos⁡4)\frac1{16}(1-\cos4)

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