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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Definitions:

Annual Compounding

Determining annual interest by taking into account both the initial amount invested and the interest it has generated in the past.

Compounded Monthly

The calculation of interest using the principal sum along with its accrued interest, with this process happening every month.

Investment

Disbursing funds or other assets with the aim of earning returns or profits.

Average Annual Rate

A financial term indicating the average amount of interest earned or paid per year over the life of an investment or loan.