Determine all rational numbers that can be written as
\[
\frac{1}{n_1} + \frac{1}{n_1 n_2} + \frac{1}{n_1 n_2 n_3} + \dots + \frac{1}{n_1 n_2 n_3 \dots n_k} ,
\]
where \( n_1, n_2, n_3 \dots, n_k \) are positive integers greater than \(1\).

The best solution was submitted by 조정휘 (수리과학과 대학원생, +4). Congratulations!

Here is the best solution of problem 2021-22.

Other solutions were submitted by 신주홍 (수리과학과 2020학번, +3), 이재욱 (전기및전자공학부 2018학번, +3), 이호빈 (수리과학과 대학원생, +3), 전해구 (기계공학과 졸업생, +3).