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

question 49

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.

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