Determine Whether the Sequence $a _ { n } = \lim _ { n \rightarrow \infty } \frac { 15 } { n ^ { 3 } } \left[ \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } \right]$

Essay

Determine whether the sequence $a _ { n } = \lim _ { n \rightarrow \infty } \frac { 15 } { n ^ { 3 } } \left[ \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } \right]$ converges or diverges. If it converges, find the limit.