For positive integer \( n \), define \( f(n) = n +\displaystyle \frac{16 + 5n - 3n^2}{4n + 3n^2} + \frac{32 + n - 3n^2}{8n + 3n^2} + \ldots + \frac{25n - 7n^2}{7n^2} \). Then, the value of \( \displaystyle\lim_{n \to \infty} f(n) \) is equal to:
\( 3 + \dfrac{4}{3} \log_e 7 \)
\( 4 - \dfrac{3}{4} \log_e \left( \dfrac{7}{3} \right) \)
\( 4 - \dfrac{4}{3} \log_e \left( \dfrac{7}{3} \right) \)
\( 3 + \dfrac{3}{4} \log_e 7 \)
