For positive integer $$n$$, define

$$f(n) = n + \dfrac{16 + 5n - 3n^2}{4n + 3n^2} + \dfrac{32 + n - 3n^2}{8n + 3n^2} + \dfrac{48 - 3n - 3n^2}{12n + 3n^2} + \cdots + \dfrac{25n - 7n^2}{7n^2}$$.

Then the value of $$\displaystyle\lim_{n \to \infty} f(n)$$ is equal to

A

$$3 + \dfrac{4}{3}\log_e 7$$

B

$$4 - \dfrac{3}{4}\log_e\left(\dfrac{7}{3}\right)$$

C

$$4 - \dfrac{4}{3}\log_e\left(\dfrac{7}{3}\right)$$

D

$$3 + \dfrac{3}{4}\log_e 7$$