A) $S(n)=\frac{4[36 n+11(n+1)]}{3 n^{2}}, \lim _{n \rightarrow \infty} S(n)=\frac{232}{3}$ B) $S(n)=\frac{4[36 n(n+1)+11(n+1)(2 n+1)]}{3 n^{2}}, \lim _{n \rightarrow \infty} S(n)=\frac{232}{3}$

Multiple Choice

$\text { Rewrite } \sum_{i=1}^{n}\left[\frac{12}{n}+\left(\frac{11 i}{n^{2}}\right) \right]\left(\frac{8 i}{n}\right) \text { as a rational function } S(n) \text { and find } \lim _{n \rightarrow \infty} S(n) \text {. }$

A) $S(n) =\frac{4[36 n+11(n+1) ]}{3 n^{2}}, \lim _{n \rightarrow \infty} S(n) =\frac{232}{3}$
B) $S(n) =\frac{4[36 n(n+1) +11(n+1) (2 n+1) ]}{3 n^{2}}, \lim _{n \rightarrow \infty} S(n) =\frac{232}{3}$
C) $S(n) =\frac{4[36 n(n+1) +11(n+1) (2 n+1) ]}{3 n^{2}}, \lim _{n \rightarrow \infty} S(n) =\frac{5}{6}$
D) $S(n) =\frac{4[36+11 n]}{3 n}, \lim _{n \rightarrow \infty} S(n) =\frac{232}{3}$
E) $S(n) =\frac{4[36 n(n+1) +11(n+1) (2 n+1) ]}{3 n^{2}}, \text { limit does not exist }$