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\[f(n)=\frac { 4n+\sqrt { 4{ n }^{ 2 }-1 } }{ \sqrt { 2n+1 } +\sqrt { 2n-1 } } \]

Function \(f : \mathbb {N \to R}\) is defined as above. Determine \(f(13)+f(14)+f(15)+...+f(112)\).

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