Let $a _ { n } = \frac { 1 + 3 ^ { n } } { 1 + 4 \cdot 3 ^ { n } }$

Essay

Let $a _ { n } = \frac { 1 + 3 ^ { n } } { 1 + 4 \cdot 3 ^ { n } }$ .
(a) Find $\lim _ { n \rightarrow \infty } a _ { n }$ .
(b) Is $\sum a _ { n }$ convergent? Justify your answer.