JEE Math Practice Question

For positive integer $n$, define \[ f(n)=n+\frac{16+5 n-3 n^{2}}{4 n+3 n^{2}}+\frac{32+n-3 n^{2}}{8 n+3 n^{2}}+\frac{48-3 n-3 n^{2}}{12 n+3 n^{2}}+\cdots+\frac{25 n-7 n^{2}}{7 n^{2}} \] Then, the value of $\lim _{n \rightarrow \infty} f(n)$ is equal to

1. A.$3+\frac{4}{3} \log _{e} 7$
2. B.$4-\frac{3}{4} \log _{e}\left(\frac{7}{3}\right)$
3. C.$4-\frac{4}{3} \log _{e}\left(\frac{7}{3}\right)$
4. D.$3+\frac{3}{4} \log _{e} 7$