MathDB
SMT 2013 Calculus #10

Source:

February 3, 2013
calculuslimitintegrationtrigonometry

Problem Statement

Evaluate lim⁡n→∞[(∏k=1n2k2k−1)∫−1∞(cos⁡x)2n2x dx]\lim_{n\to\infty}\left[\left(\prod_{k=1}^{n}\frac{2k}{2k-1}\right)\int_{-1}^{\infty}\frac{(\cos x)^{2n}}{2^x} \, dx\right].
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