Evaluate the sum \[ \sum_{n=1}^{\infty} \frac{n \sin n}{1+n^2}. \]
The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!
Here is his Solution of Problem 2011-1.
A solution for an incorrect version of the problem was submitted by 구도완 (해운대고등학교 3학년).
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.
Let X be a finite set of points on the plane such that each point in X is colored with red or blue and there is no line having all points in X. Prove that there is a line L having at least two points of X such that all points in L∩X have the same color.
The best solution was submitted by Minjae Park (박민재), 한국과학영재학교 (KSA). Congratulations!
Here is his Solution of Problem 2010-20.
Prove that there is a constant C such that
\(\displaystyle \sup_{A<B} \int_A^B \sin(x^2+ yx) \, dx \le C\)
for all y.
The best solution was submitted by Minjae Park (박민재), KSA (한국과학영재학교) 3학년. Congratulations!
Here is his Solution of Problem 2010-13.
Alternative solutions were submitted by 정진명 (수리과학과 2007학번, +3), 정성구 (수리과학과 2007학번, +3), 심규석 (수리과학과 2007학번, +3). Three incorrect solutions were submitted (서**, 정**, Ver**).