Rewrite $\sum _ { i = 1 } ^ { n } \frac { 4 i + 2 } { n ^ { 2 } }$

question 26

Multiple Choice

Rewrite $\sum _ { i = 1 } ^ { n } \frac { 4 i + 2 } { n ^ { 2 } }$ as a rational function S(n) and find $\lim S ( n )$ .

• A) \(S ( n ) = \frac { 2 ( n + 1 ) + 2 } { n } , \lim _ { n \rightarrow \infty } S ( n ) = 2\)
• B) \(S ( n ) = \frac { 2 ( n + 1 ) + 2 } { n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)
• C) \(S ( n ) = \frac { 2 ( n + 1 ) + 2 } { n } , \lim _ { n \rightarrow \infty } S ( n ) = 4\)
• D) \(S ( n ) = \frac { 2 ( n + 1 ) 2 } { n } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)
• E) \(S ( n ) = \frac { 2 n ( n + 1 ) + 2 } { n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = 2\)

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