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Putnam 1965 B1

  • Session B

Evaluate lim⁡n→∞∫01∫01⋯∫01cos⁡2(π2n(x1+x2+⋯+xn))dx1dx2⋯dxn.\lim_{n \to \infty} \int_0^1 \int_0^1 \cdots \int_0^1 \cos^2 \left(\frac{\pi}{2n}(x_1 + x_2 + \cdots + x_n)\right) dx_1 dx_2 \cdots dx_n.

Dataset text Putnam-AXIOM. Quoted with source.

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