Solution: 2011-8 Geometric Mean

Let f be a continuous function on [0,1]. Prove that \[ \lim_{n\to \infty}\int_0^1 \cdots \int_0^1 f(\sqrt[n]{x_1 x_2 \cdots x_n } ) dx_1 dx_2 \cdots dx_n = f(1/e).\]

The best solution was submitted by Kang, Dongyub (강동엽), 전산학과 2009학번. Congratulations!

Here is his Solution of Problem 2011-8.

Alternative solutions were submitted by 김치헌 (수리과학과 2006학번, +3), 어수강 (홍익대학교 수학교육과 2004학번, +3).

(Here is a Solution by Chiheon Kim for Problem 2011-8.)

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