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.