Strange sum

Calculus Level 3

If

\[ \frac{ 1 }{ 1^2 + 4 } + \frac{ 1}{2^2 + 8 } + \frac{ 1 }{ 3^2 + 12 } + \ldots = \frac { p}{q}, \]

where \(p\) and \(q \) are coprime positive integers, what is \( p + q \)?

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