Rewrite $\sum _ { i = 1 } ^ { n } \frac { 7 i ^ { 3 } } { n ^ { 8 } }$

question 206

Multiple Choice

Rewrite $\sum _ { i = 1 } ^ { n } \frac { 7 i ^ { 3 } } { n ^ { 8 } }$ as a rational function S(n) and find $\lim _ { n \rightarrow \infty } S ( n )$ .

• A) \(S ( n ) = \frac { 7 ( n + 1 ) ^ { 2 } } { 4 n ^ { 6 } } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)
• B) \(S ( n ) = \frac { 7 n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } , \lim _ { n \rightarrow \infty } S ( n ) = 7\)
• C) \(S ( n ) = \frac { 7 ( n + 1 ) ^ { 2 } } { 4 n ^ { 6 } } , \text { the limit does not exist }\)
• D) \(S ( n ) = \frac { 7 ( n + 1 ) ^ { 2 } } { 4 n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = \frac { 7 } { 4 }\)
• E)\(S ( n ) = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 28 } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)

---

Definitions:

Eyes

Sensory organs of vision that allow for the perception of light, shapes, colors, and depth, playing a crucial role in human interaction and understanding of the environment.

Nonverbal Cues

Consist of all the ways in which people communicate without words, including gestures, facial expressions, and body language.

Demographics

Statistical data relating to the population and particular groups within it, often used for marketing and planning purposes.

Emotions

Emotions are complex psychological states involving an individual's subjective experience, physiological response, and behavioral or expressive reaction.