What? I'm stumped!

Calculus Level 4

\[ \displaystyle \Large \lim_{(n,r) \to (\infty, \infty)} \frac {\displaystyle \prod_{k=1}^r \left ( \displaystyle \sum_{i=1}^n i^{2k-1} \right ) }{ n^{r+1} \displaystyle \prod_{k=1}^{r-1} \left ( \displaystyle \sum_{i=1}^n i^{2k} \right ) } = \, ? \]

Give your answer to 3 decimal places.


This is an original problem.
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