\[\begin{eqnarray} f(13) + f(14) + f(15) + f(16) + \cdots + f(112) \end{eqnarray} \]

Given that \(f\) is a real function such that \( f(n) = \dfrac{4n + \sqrt{4n²-1}}{ \sqrt{2n+1} + \sqrt{2n-1}} \) for \(n\) real positive integer. Find the value of the expression above.

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