Can you sum this?

Algebra Level 4

\[\large{S = \dfrac{3^2 + 1}{3^2 - 1} + \dfrac{5^2 + 1}{5^2 - 1} + \dfrac{7^2 + 1}{7^2 - 1} + \ldots + \dfrac{2015^2 + 1}{2015^2 - 1}}\]


If \(S\) can be expressed as \(\dfrac{A}{B}\) for positive coprime integers \(A,B\), then find the value of \(A+B\).

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