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

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

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

Definitions:

Determine Whether the Sequence an=lim⁡n→∞15n3[n(n+1)(2n+1)6]a _ { n } = \lim _ { n \rightarrow \infty } \frac { 15 } { n ^ { 3 } } \left[ \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } \right]an​=limn→∞​n315​[6n(n+1)(2n+1)​]

Definitions:

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