Limits Continuity And Differentiability

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 \(\mathop {\lim }\limits_{n \to \infty } f\left( n \right)\) is equal to :