# 2016-19 Zeta function

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.

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