Find the Following Limit of the Sequence As $n$ Approaches Infinity, If It Exists

Multiple Choice

Find the following limit of the sequence as $n$ approaches infinity, if it exists.
$$a _ { n } = \frac { 1 } { n } \left( n + \frac { 4 } { n } \left[ \frac { n ( n + 1 ) } { 6 } \right] \right)$$

A) $\frac { 2 } { 3 }$
B) $\frac { 8 } { 3 }$
C) $\frac { 5 } { 3 }$
D) $\frac { 11 } { 6 }$
E) The limit does not exist.