Daily Archives: September 18, 2017

Solution: 2017-13 Infinite series with recurrence relation

Let \(a_0 = a_1 =1\) and \(a_n = n a_{n-1} + (n-1) a_{n-2}\) for \(n \geq 2\). Find the value of
\[
\sum_{n=0}^{\infty} (-1)^n \frac{n!}{a_n a_{n+1}}.
\]

The best solution was submitted by Choi, Daebeom (최대범, 수리과학과 2016학번). Congratulations!

Here is his solution of problem 2017-13.

Alternative solutions were submitted by 국윤범 (수리과학과 2015학번, +3), 김동률 (수리과학과 2015학번, +3), 김태균 (수리과학과 2016학번, +3), 유찬진 (수리과학과 2015학번, +3), 윤준기 (전기및전자공학부 2014학번, +3), 이본우 (2017학번, +3), 이태영 (수리과학과 2013학번, +3), 장기정 (수리과학과 2014학번, +3, solution), 조태혁 (수리과학과 2014학번, +3, solution), 최인혁 (물리학과 2015학번, +3), Huy Tung Nguyen (수리과학과 2016학번, +3), 김기택 (수리과학과 2015학번, +2), 이재우 (함양고등학교 2학년, +2), 정의현 (수리과학과 2015학번, +2).

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