Rewrite $\sum _ { i = 1 } ^ { n } \frac { 4 i + 2 } { n ^ { 2 } }$

Multiple Choice

Rewrite $\sum _ { i = 1 } ^ { n } \frac { 4 i + 2 } { n ^ { 2 } }$ as a rational function S(n) and find $\lim S ( n )$ .

A) $S ( n ) = \frac { 2 ( n + 1 ) + 2 } { n } , \lim _ { n \rightarrow \infty } S ( n ) = 2$
B) $S ( n ) = \frac { 2 ( n + 1 ) + 2 } { n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = 0$
C) $S ( n ) = \frac { 2 ( n + 1 ) + 2 } { n } , \lim _ { n \rightarrow \infty } S ( n ) = 4$
D) $S ( n ) = \frac { 2 ( n + 1 ) 2 } { n } , \lim _ { n \rightarrow \infty } S ( n ) = 0$
E) $S ( n ) = \frac { 2 n ( n + 1 ) + 2 } { n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = 2$