If $\lim_{n \to \infty} \sum_{r=1}^{n} \frac{k^r}{1 \times 3 \times 5 \times 7 \times 9 \times \dots \times (2r+1)} = 1$ …

Mathematics

Problem

If

\lim_{n \to \infty} \sum_{r=1}^{n} \frac{k^r}{1 \times 3 \times 5 \times 7 \times 9 \times \dots \times (2r+1)} = 1

then

k^2 =

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