Rewrite $\sum _ { i = 1 } ^ { n } \frac { 5 i ^ { 3 } } { n ^ { 5 } }$

question 101

Multiple Choice

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

• A) \(S ( n ) = \frac { 5 ( n + 1 ) ^ { 2 } } { 4 n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = \frac { 5 } { 4 }\)
• B) \(S ( n ) = \frac { 5 n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } , \lim _ { n \rightarrow \infty } S ( n ) = 5\)
• C) \(S ( n ) = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 20 } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)
• D) \(S ( n ) = \frac { 5 ( n + 1 ) ^ { 2 } } { 4 n ^ { 3 } } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)
• E) \(S ( n ) = \frac { 5 ( n + 1 ) ^ { 2 } } { 4 n ^ { 3 } }\) the limit does not exist

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