2022-01 Alternating series

Evaluate the following:
\[
\frac{1}{1^2 \cdot 3^3 \cdot 5^2} – \frac{1}{3^2 \cdot 5^3 \cdot 7^2} + \frac{1}{5^2 \cdot 7^3 \cdot 9^2} – \dots
\]

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