# Concluding 2010 Fall

Thanks all for participating POW actively. Here’s the list of winners:

1st prize: Kim, Chiheon (김치헌) – 수리과학과 2006학번

2nd prize: Park, Minjae (박민재) – 한국과학영재학교 (KAIST 2011학번 입학예정)

3rd prize: Jeong, Jinmyeong (정진명) – 수리과학과 2007학번.

Congratulations!

In addition to these three people, I selected one more student to receive 2 movie tickets.

Jeong, Seong-Gu (정성구) – 수리과학과 2007학번.

김치헌 (2006학번) 28 pts
박민재 (KSA) 25 pts
정진명 (2007학번) 19 pts
정성구 (2007학번) 16 pts
서기원 (2009학번) 9 pts
심규석 (2007학번) 9 pts
권용찬 (2009학번) 3 pts
정유중 (2006학번) 3 pts
진우영 (KSA) 3 pts
서영우 (2010학번) 2 pts
오상국 (2007학번) 2 pts
GD Star Rating

# Solution: 2010-21 Limit

Let $$a_1=0$$, $$a_{2n+1}=a_{2n}=n-a_n$$. Prove that there exists k such that $$\lvert a_k- \frac{k}{3}\rvert > 2010$$ and yet $$\lim_{n\to \infty} \frac{a_n}{n}=\frac13$$.

The best solution was submitted by Chiheon Kim (김치헌), 수리과학과 2006학번. Congratulations!

Here is his Solution of Problem 2010-21.

Alternative solutions were submitted by 한대진 (신현여중 교사, +2), 이승훈 (연세대학교 경제학과 06학번, +2).

GD Star Rating