Rewrite $\sum _ { i = 1 } ^ { n } \left[ \frac { 3 } { n } + \left( \frac { 4 i } { n ^ { 2 } } \right) \right] \left( \frac { 4 i } { n } \right)$

question 109

Multiple Choice

Rewrite $\sum _ { i = 1 } ^ { n } \left[ \frac { 3 } { n } + \left( \frac { 4 i } { n ^ { 2 } } \right) \right] \left( \frac { 4 i } { n } \right)$ as a rational function S(n) and find $\lim _ { n \rightarrow \infty } S ( n )$ .

• A) \(S ( n ) = \frac { 2 [ 9 n ( n + 1 ) + 4 ( n + 1 ) ( 2 n + 1 ) ] } { 3 n ^ { 2 } } \text {, limit dos not exist }\)
• B) \(S ( n ) = \frac { 2 [ 9 + 4 n ] } { 3 n } , \lim _ { n \rightarrow \infty } S ( n ) = \frac { 34 } { 3 }\)
• C) \(S ( n ) = \frac { 2 [ 9 n + 4 ( n + 1 ) ] } { 3 n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = \frac { 34 } { 3 }\)
• D) \(S ( n ) = \frac { 2 [ 9 n ( n + 1 ) + 4 ( n + 1 ) ( 2 n + 1 ) ] } { 3 n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = \frac { 5 } { 6 }\)
• E) \(S ( n ) = \frac { 2 [ 9 n ( n + 1 ) + 4 ( n + 1 ) ( 2 n + 1 ) ] } { 3 n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = \frac { 34 } { 3 }\)

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Definitions:

Part Performance

An equitable doctrine that allows a contract, typically not in writing, to be enforced if one party has taken significant steps to perform their part of the agreement.

Interest in Land

Legal rights or investments in real estate that involve ownership or other financial claims on the property.

Verbal Evidence

Evidence presented in the form of words, spoken or written, as opposed to physical evidence or demonstrations, used in legal proceedings.

Statute of Frauds

A legal principle that requires certain types of contracts to be in writing in order to be enforceable.