A) $S(n)=\frac{9(n+1)^{2}}{4 n^{2}}, \lim _{n \rightarrow \infty} S(n)=\frac{9}{4}$ B) $S(n)=\frac{9 n^{2}(n+1)^{2}}{4}, \lim _{n \rightarrow \infty} S(n)=9$

question 32

Multiple Choice

$\text { Rewrite } \sum_{i=1}^{n} \frac{9 i^{3}}{n^{5}} \text { as a rational function } S(n) \text { and find } \lim _{n \rightarrow \infty} S(n) \text {. }$

• A)\(S(n)=\frac{9(n+1)^{2}}{4 n^{2}}, \lim _{n \rightarrow \infty} S(n)=\frac{9}{4}\)
• B)\(S(n)=\frac{9 n^{2}(n+1)^{2}}{4}, \lim _{n \rightarrow \infty} S(n)=9\)
• C)\(S(n)=\frac{n^{2}(n+1)^{2}}{36}, \lim _{n \rightarrow \infty} S(n)=0\)
• D)\(S(n)=\frac{9(n+1)^{2}}{4 n^{3}}, \lim _{n \rightarrow \infty} S(n)=0\)
• E) \(S(n)=\frac{9(n+1)^{2}}{4 n^{3}}, \text { the limit does not exist }\)

---

Definitions:

Opportunity Cost

The expense incurred by not choosing the second-best option during a decision-making process.

Sweaters

A knitted garment typically made of wool, cotton, or synthetic yarn, worn over the upper body for warmth.

Cookies

Small pieces of data sent from a website and stored on a user's computer by the user's web browser while the user is browsing.

Specialization

The process in economics and production where individuals or entities focus on a narrow area of expertise to increase efficiency and output.