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)\(S ( n ) = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 28 } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)

Analyze the economic transitions in Europe, including shifts from peasant labor obligations to other forms of taxation or rent.

Recognize the contribution of technological advances and industrial growth to societal changes, including the decrease in death rates and the beginning of the Industrial Revolution.

Identify the social and economic conditions of peasants and other classes during the eighteenth century.

Comprehend the evolving roles and job opportunities for women in society.

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