Let
\[
P(k) = \sum_{i_1=1}^{\infty} \dots \sum_{i_k=1}^{\infty} \frac{1}{i_1 \dots i_k (i_1 + \dots + i_k)}
\]
for a positive integer \( k \). Find \( \zeta(k+1) / P(k) \), where \( \zeta \) is the Riemann-zeta function.

The best solution was submitted by Lee, Sangmin (이상민, 수리과학과 2014학번). Congratulations!

Here is his solution of problem 2016-19.

Alternative solutions were submitted by 신준형 (수리과학과 2015학번, +3), 장기정 (수리과학과 2014학번, +3), 이종원 (수리과학과 2014학번, +3), 김태균 (2016학번, +3).