Let \(\{a_n\}\) be a sequence of non-negative reals such that \( \lim_{n\to \infty} a_n \sum_{i=1}^n a_i^5=1\). Prove that \[ \lim_{n\to \infty} a_n  (6n)^{1/6} = 1.\]

The best solution was submitted by 고경훈 (2015학번). Congratulations!

Here is his solution of Problem 2015-3.

Alternative solutions were submitted by 이종원 (수리과학과 2014학번, +3), 김경석 (2015학번, +3), 김기현 (수리과학과 2012학번, +3), 엄태현 (수리과학과 2012학번, +3), 이명재 (수리과학과 2012학번, +3), 정성진 (수리과학과 2013학번, +3), 진우영 (수리과학과 2012학번, +3), 최인혁 (2015학번, +3), 이수철 (수리과학과 2012학번, +3), 국윤범 (2015학번, +3), 박지현 (경상고등학교 2학년, +3). One incorrect solution was submitted (SKB).