Find the Limit of the Sequence (If It Exists) $\alpha _ { n } = \frac { 4 n ^ { 2 } + 1 } { 2 n }$

Multiple Choice

Find the limit of the sequence (if it exists) . $\alpha _ { n } = \frac { 4 n ^ { 2 } + 1 } { 2 n }$

A) $\lim_ { n \rightarrow \infty } \alpha _ { n } = - 4$
B) $\lim _ { n \rightarrow \infty } \alpha _ { n } = \frac { 1 } { 2 }$
C) $\lim _ { n \rightarrow \infty }\alpha _ { n } = 4$
D) $\lim_ { n \rightarrow \infty } \alpha _ { n } = 0$
E) $\lim_ { n \rightarrow \infty } a _ { n } = \infty$