good enough for late time

Calculus Level 4

\[\large \frac {\large 1 - 2^{-2} + 4^{-2} - 5^{-2} + 7^{-2} - 8^{-2} + \ldots }{1+ 2^{-2} - 4^{-2} - 5^{-2} + 7^{-2} + 8^{-2} - \ldots } = \ ? \]

Give your answer to three decimal places.

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